Remember that East passed his partner's opening bid and has aleady turned up with the ♥A. West is therefore marked with the missing high cards.  Draw the trumps with the aid of 2 finesses and then cash the ♦AK. If you are lucky, the ♦Q will fall and now you have to tackle the club suit. Since West is marked with the Queen, start by leading the Knave from hand. If it is covered, you can then finesse East for the ♣T. 

The key fact to notice is that South has given up on spades.   There is no reason for South to do so holding four to the ace, as ducking another spade will allow cashing two spades when either defender gets in.  Ergo spades must be 5-2 (or 6-1).

And if South had long spades, they would still be useful if South had an entry.  You can deduce therefore that the club ace is with North.

Clearly the defence can set up some diamonds but you can always make your contract.  If you play out clubs you will get two club tricks to go with one spade, four hearts, and two diamonds - nine tricks, as required.  If you can get a second spade trick you are even better off.  So you win the diamond and try leading a club through North, who ducks.  Now you can set up your ninth trick in either spades or clubs.  North is not likely to duck clubs again, so you switch to spades and lead towards the ♠Q4.  If South ducks that you will win and go back to clubs and you have ten tricks before they set up diamonds.

Was there a stronger defence?  The answer is yes - North should have risen with the club ace on the first round, and played a second spade.   This would be vital if South had the club king and declarer the club queen.  It might also be vital if South's spades were king high and declarer had the ace.  

What do make of the lead? The inferences to draw are that West does not hold ♠ AK as else he would surely have led one. Also the ♦Q looks certain to be offside. If those inferences are correct, the contract looks to have reasonable play with correct technique. Win the lead, draw trumps (in 3 rounds as it happens) finishing in dummy, before playing a club to your King. Let's say that loses. Now the link between the defenders has effectively been cut whenever the spades break 6-1. You just give up a diamond and the defence can't get at their second spade winner.

A little counting helps here. Declarer is marked with a singleton heart and four spades leaving eight "other" cards. Declarer's two more likely distributions are 4-1-5-3 or 4-1-4-4.  In the first case there is a danger that unless clubs are broached immediately, declarer will be able to draw trumps and discard a club from dummy on a fifth diamond. In the second case, partner has a doubleton club and may be able to obtain a ruff.

It is clearly right to overtake the partner's lead and shift to a low club, showing strength, at trick two. Your play works out beyond your wildest dreams because the are the unseen hands are as above:

As it happens partner wins the first club presumably with the jack, cashes the ♣K, and leads a club to your ace. Continuing with your sharp play, you play a 13th club and when partner uppercuts the ♠A out of the dummy with the ♠10, your J98 of trumps promote to the setting trick,

Tip:

When declarer turn up with an early singleton (hearts) and the length of at least one other of the declarer's suits is marked on the bidding (spades), consider the likely distribution of the remaining cards and defend accordingly.

Consider the diamond suit, West would not underlead the Ace so East has AK.  Presumably he lacks the Queen else he would have played that card so West holds the Queen but not the Knave for he would not have led low from QJ.  The spade honours must be split - if East held both he would have had an opening bid.  Hence the likelihood is that West holds both the ♥Q and ♣Q else again East would have opened the bidding.

So win the ♣A and run the ♥6 at trick 3 in case west holds 4.  Then draw trumps and play clubs from the top - hoping to make 3 club tricks.  You hope the layout is as shown.

Note that the light take-out double backfires against a declarer who is listening to the bidding

The two pieces of jigsaw that need to be put together are that North has the ♥K and that South has not lead from the ♦AK or from the ♣AK.   It is quite a deep position to judge not to lead an AK if you have one, so we deduce that North has an honour in each of diamonds and clubs, to go with the ♥K, and so North cannot hold the ♠Q.  We therefore play trumps from the top (the finesse cannot work) and justice is served when the queen falls and we can draw all four trumps.  Now comes the question of how to play the club suit?  Clearly North has only three cards in the minors, and we cannot play diamonds without finding ourselves forced, so it has to be clubs and we see we can rarely avoid losing three club tricks. It is important however not to lose four club tricks and we can do this only if North has a singleton honour.  So the next play (necessary too for two club tricks) is a small club from both hands and again justice seems to be served when North wins the king. They play diamonds and then another heart, which we ruff.  We should now duck another club (no joy), and in due course knock out the ♣ A to obtain 8 tricks and the possibility of a few match-points.  In fact escaping for -50 gets just above average and you see that they can always make 3♥ (by setting up the ♦T for a trick if not allowed a spade ruff).

You have 9 red suit tricks and you can force an additional trick in spades.  What can go wrong?  A problem may arise if the trumps break 4-1.  You will have to ruff the second club lead and draw trumps and this will leave you with only one trump and 2 spades to knock out.  If you lose the first spade to West, another club through your King will sink the contract.  Fortunately, you have taken note of the bidding, which clearly marks East with the ♠A.  Having drawn trumps, play the ♠K from hand.  When East takes the Ace, he cannot attack clubs profitably from his side.  You just lose one club and 2 spades.  The distribution you have to guard against is as shown.

The bidding marks the heart Ace and spade King with West so you have a neat play for your contract. At trick 2 you must discard a spade from dummy. Now 2 rounds of trumps finishing in hand allows you to lead a low heart towards the King. If West rises with the Ace. the King of hearts provides a parking place for you spade loser, so West must duck. Now you return to hand with a trump, cash the winning club throwing aheart from the table and exit with a heart. West wins but is endplayed!

You almost certainly have 2 club losers so you must avoid losing 2 trump tricks.  The bidding almost certainly places the ♠K with East and you must not take a first round spade finesse.  Laying down the  ♠A will save you when the layout is as shown.

The opening lead tells you that East has one card remaining which is higher than the 5.  You should guess the position correctly by rising with the K♥ as if West held Q975 originally, he should have led the queen to the third trick, as this enables the defense to take 4 heart tricks whenever declarer holds 10x.

However, you might have avoided this guess altogether if you had dropped the 8♥ at trick 1.  This would probably have induced East into returning a heart at trick 2, thinking that his partner had led from a 5 card suit.

You need to pay attention to the spot cards in spades.  East has played the 8♠ at trick 1 (probably from a doubleton).  This means you can establish an extra trick in the spade suit.  Your plan should be as follows:

Win A♠. Draw trumps - it turns out that West has a singleton and East Jxx.  Now play 10♠ from hand.

West wins and switches to the J♦.

Rise with the A♦ and lead 9♠ from dummy, discarding a club.  West can win, put his partner in with K♦ to play a club through - but you rise with A♣, ruff a diamond, and discard your losing club on 7♠ which is now a winner.  This way you make your contract regardless of the position of either minor suit King.  A simple loser on loser play.  How many were tempted into taking both minor suit finesses and then complaining about their bad luck?

You look to have a club loser in addition to the Ace of trumps.  However, if you could force a club lead from the player that wins the ♠A, your chances would greatly improve.  What is the best way to do this?  Try the effect of crossing to dummy to lead the ♠J.  If East has ♠Ax he may well duck, perhaps playing his partner for a singleton King or Queen of spades.  If he ducks, you can cash the other diamond before exiting with a trump.  This will force the defence to give you a ruff and discard or open up the clubs.  On the actual layout, East has a singleton spade so has to take the Ace on the first round.  Does this spell certain defeat?  At the table, the contract still made.  East was beset with the notion from declarers play that partner held a key holding in spades - Qx say.  When in with the ♠A, East played a fourth round of hearts to promote partners presumed ♠Q and the ensuing ruff and discard handed the contract to declarer.  South did well to play as he did; the defence could hardly go wrong if he had started the spades from hand.  A mark of a good player is that he constantly sows seeds of doubt in defenders minds.

Surely West must hold all the missing hearts to justify his double. If that is the case, can you make him pay? Win the ♦A shedding a spade from hand. Now take your winning clubs, discarding a spade and a diamond from dummy. Now a spade ruff on the table and a diamond ruff in hand is followed by a further spade, ruffed on the table with the ♥T. Then cash the ♥A (your ninth trick) and exit with a diamond, discarding your losing club. West is endplayed and must concede a trick to your Knave of hearts.

You definitely need the ♥A onside to have a chance. If the clubs break 3-3 then you will be able to set up a club trick for a heart discard. The bidding makes it fairly certain the West has very long diamonds, so you also have a chance of  playing for a squeeze chance in addition to the 3-3 club break. Ruff the diamond and draw trumps before playing Ace and a low club from hand. If West rises with a doubleton honour, he will have no sensible exit other than Ace and another heart. Win the King of hearts in dummy and run the trumps. On the last trump, East has to throw a winning heart or give up the club suit. 

Your combined trumps will take care of the minors so you must avoid 2 heart losers.  Fortunately, the bidding indicates that West started with at most 2 hearts, so the contract is assured.  After the ♠A, play a trump to dummy, ruff a club, ♦A and another club ruff.  Then ♦K, diamond ruff and another club ruff eliminates the minors from the N/S hands.  Now a heart to the Ace and a second heart to the Queen is a sure winning line as either the ♥K is with East or else West will win with a doubleton ♥K and then be forced to concede a ruff and discard, so your remaining heart loser disappears.

Whenever a player pre-empts and then doesn't lead his suit, you should draw the inference that the lead is a singleton. Therefore a club ruff is threatened. Can you avoid this? The solution is to rise with the ♣Q on the opening lead and cash the ♥A discarding the ♣A from hand. Now you can ruff a heart to hand and lead a top trump. If the defence play another club, you can ruff high and draw trumps, just losing the ♠A later

You only have winners outside the trump suit so this hand hinges on finding the ♥Q. This is a time for some detective work. From the bidding and early play, LHO is marked with five spades and not too many diamonds. Hence he can't have short clubs. Before playing trumps, it can't cost to play more clubs from dummy. On the second round of clubs, you get lucky in that East shows out! This marks West with 5–5 in the black suits, and heart shortness. If West has two hearts, it means only one diamond. That would give East seven diamonds, and he would likely have bid the first time. With West’s shape pretty much marked (5125), hence you should play the ♥K and then finesse against East’s ♥Q.

This is an example of a second degree assumption.  If you are to have any chance of making the contract, the ♦A must be with West.  If this is the case he cannot hold the ♠A - else he would have had enough to open the bidding.  Since you can only lead trumps once from dummy, you should win the heart and lead a spade, playing the King if East plays low.  You hope the full layout is akin to that shown. 

It looks like the lead is from ♥ AQxxx and since West did not overcall 1♥, he is most unlikley to hold the ♠A, so establishing spade tricks is not really an option. In fact, West's silence means that East is quite likely to hold both the missing minor suit honours. Best play is to run the ♦9 at trick 2. When this holds, you can take the club finesse and return in diamonds to pick up 5 tricks in that suit, thus making the contract.

You already know a lot about the shape of the defenders hands. If you win the ♦A, then ruff a diamond and play a trump to dummy and ruff the last diamond with the ♣A - you will know the exact shape of West's and hence East's hand. If West has 2 cards in each minor and therefore 3 hearts then you take the heart finesse as your only chance, but if West proves to have three clubs and a doubleton heart, you play him for ♥Q doubleton, as otherwise you will always have a heart loser. 

What do you infer from the bidding and opening lead? Surely West would have led a top heart if holding the AK or AKQ, hence it is reasonable to place East with a top heart (probably the King). Since he passed his partner's opening bid, he can safely be assumed not to have another King. Therefore win the lead and lay down the ♠A. If the King drops you have 10 tricks. If the ♠K remains at large, take the diamond finesse to dispose of a heart loser.

The bidding strongly suggests that West holds the A♠ in a six card suit, in which case you need to make 4 heart tricks and 4 club tricks. The only way to make 4 heart tricks is to find the suit beaking 3-3. Counting West's hand means you need him to be 6322. There is no way to bring in 4 club tricks if East holds Qxxx so you need to play West for Qx. Cash the ♣K and play a club to the Ace. When the Queen drops, you can take 4 tricks in the suit, to go with 4 hearts and 4 diamonds.

Cash dummy’s two high clubs, discarding a heart, and ruff a club. Assuming everyone follows, cross back to the ♦A (it doesn’t hurt to lead the jack) and ruff dummy’s last club. If everyone follows, you have a count of the hand. West is 0724 and East 4234. You now have a claim. Cash the ♠Q and play the ♦K. If both follow low, exit a diamond to East’s queen and take the last two tricks with the ♠A 10. If West’s ♦Q drops doubleton, you still have a spade loser, but you make four. If, when you ruff dummy’s last club, West shows out, West is known to have a 0733 shape and East is 4225. You are now reduced to finding East with the ♦Qx. You cannot make the contract at this point if West started with the Qxx.

There are 2 possibilities to dispose of your second heart loser. One way would be to take a winning club finesse and the other way would be to endplay West. Given that West is heavily odds on to hold ♥AJ, then the second way is preferred. Ruff the third diamond, draw trumps and eliminate clubs. If trumps are 2-1 cross to dummy to play a heart to the Queen. If trumps are 3-1 just exit with the ♥Q. West will win and have to concede a ruff and discard or lead from his ♥J. 

Two tricks in the bag and the Ace of trumps still to come but beyond that prospects are bleak. South surely has ♠ KQxxx and there can be minor suit tricks for your side. One possibility is that South has falsecarded in hearts and that partner has a doubleton. Then all you need is for partner to have a spade higher than the 8. You lead a third heart but both South and West follow. South ruffs his winning heart in dummy and leads a trump. This is your last chance. Although you know partner will be out of trumps after this trick, South doesn't have that information. Rise with the Ace of trumps and lead another heart. On a good day declarer will ruff high and lay down his remaining top trump, hoping the Knave will fall. You will then have conjured up a second trump trick from thin air.

You have 9 obvious tricks and can look to spades to provide a tenth. It looks tempting to finesse the Queen at trick one but first you should check the defensive carding methods. If you are told that the Jack denies a higher honour, you have a strong indication that the finesse will fail. Best is to rise with the Ace at trick one and draw trumps before leading a spade towards dummy. If West has led from KJTxxx (he isn't barred from playing a misleading card at trick one) he will most likely rise with the King, pleased that his subterfuge at trick one seems to have worked. Now your Queen will be good for a diamond discard. If West plays low on the second spade, you intend to duck and play East for ♠Kx to again establish the ♠Q as your tenth trick. A simple play but the moral is that when opponents opening lead is a J,T or 9, it is important to know what the lead can be from on their methods. You can always ask!

[And sometimes West will have opened on a seven card spade suit and you might drop a singleton king]