1NT, Pass, 3NT. Pass, Pass, Pass.

North is the dealer and has to bid first.With a balanced hand and 13 points he opens 1NT. East has nothing to bid with just 6 points so passes. South has 13 points. 1NT shows at least 12 points. So N/S must have at least 25 points between them and this should be enough for "Game." South bids 3NT and West, North & East all pass thus ending the auction. East makes the opening lead, say  4C and the South hand is put down as Dummy after the lead is made.North (the declarer) has to make nine tricks and should make at least two spades, five diamonds and two clubs.

1NT, Pass, 4H, Pass, Pass, Pass.

East with 12 points and a balanced hand, bids 1NT. South who does not have enough points to bid passes.West has 13 points and six hearts, worth a game bid. East must have at least two hearts to open 1NT, so West knows it should be best to play in hearts (as they have at least 8 hearts between them) and bids 4H, a game contract needing ten tricks. As West is Declarer it is North to lead. North leads QS which holds and continues with JS but West can trump.West should manage 10 tricks, but with skill can make 11 by ruffing the losing diamondin dummy and losing just one spade and one heart.

1NT, Pass, 2NT, Pass, 3NT, Pass, Pass,Pass.

South is the dealer, with a balanced 14 points. South opens 1NT and West with 10 points passes. North has 12 points, if South has 12 this is not really enough for game (12 + 12 = 24), but South may have 13 or 14 points. North bids 2NT asking South to bid a game if maximum. South has 14 points, so bids 3NT, West, North & East all pass. West leads the AC, KC, QC, but whatever West plays next South can only lose one more trick to the AD (3NT makes  9 tricks)

1NT, Pass, 2S, Pass, Pass, Pass.

West has 14 balanced points and opens 1NT. North has 11 points and cannot find a bid. East knows that E/W have at most 17 points (14 + 3 = 17)  East's only asset is the six card spade suit. With spades as trumps the hand is more useful, so East bids 2S as a "Weakness Take Out" of 1NT. With skill  East can just manage to take eight tricks in 'Two Spades'.

Pass, 1NT, Pass, 3S, Pass, 3NT, Pass, Pass, Pass.

North passes, East with 14 points bids 1NT and South passes. West with 14 points knows that E/W should bid game but is not sure whether it should be in Spades or No Trumps, so West bids 3S (Forcing with five spades) to ask East to choose. Holding only two spades East bids 3NT. South leads the four of hearts. Win with the Jack of hearts and count your tricks. Play the clubs first to set up two tricks, plus two spades, three hearts and two diamonds. (10 Tricks). 

1NT, Pass, 3H, Pass, 4H, Pass, Pass, Pass.

When partner opens 1NT North knows that N/S should be playing in "Game"  but perhaps hearts will be better than no trumps, so North bids 3H to consult partner. South holding three hearts bids the game 4H. A good decision as 3NT should not make (look at the diamonds). Even though East has a trump trick there are only three losers (two diamonds and one heart). Try counting your tricks to check. 

Pass, Pass, 1NT, Pass, Pass, Pass. 

A simple auction since North does not have enough points to open the bidding or to respond to partners 1NT opening bid. When partner opens 1NT with a balanced hand and 0 - 10 points you should pass (14 + 10 = 24) as you have not got enough points for a game. West should lead the 5C (Fourth highest in his longest suit). South quickly takes seven tricks (four spades & three Clubs) and might come to an eighth trick in the end if E/W discard their winners.

1NT, Pass, 6NT, Pass, Pass, Pass.

It will take East a long time to count all those points as 23 is more than usual. Knowing that E/W must have at least 35 points, possibly more, a brave East bids 6NT and a nervous West can make 12 tricks or even 13. South has what is called a "Yarborough" that is no card higher than a nine. The Duke of Yarborough bet 1000 to 1 against this happening, a good bet as the true odds are 1827 to 1.