To define Splinter bids, they are any unnecessarily high jump bids, in support of last suit that Partner bid. This can be very valuable in showing a singleton or void. 

• It enables Partner to value an Ace in the Splinter suit (i.e A532)  which is a good holding to have, or KQ in the splinter suit, which is poor holding opposite a singleton, or  7542 (say), which a fabulous holding. With this Holding, since you don’t hold any points In the Splinter suit, it evaluates as a 30 point pack. (More later) 
• With KQ, opener bidder will generally sign off. With the good holdings, try to Cue bid, if practical (preferably an ace). Note on the hands below, we are NOT jumping to 4NT necessarily.  Better, very often, to Cue Bid. If you wish, play Splinter bids in the minors, as well.     

Examples             In these examples, Partner has opened 1♥ - do you splinter or not is the question

I like 3♠ on this hand, showing a singleton spade. It is an unnecessarily high jump,   1♠ would be the normal bid (say 6-16 points); 2♠ would be the normal very strong bid (Normal, Unless you follow Andrew R, where he may play that as weak!), and therefore 3♠ doesn’t have to mean spades. If Partner signs off in 4♥ I think you should pass on this hand. Partner may not have an Ace to cue  bid. E.g.   ♠K Q 7     ♥ A Q 6 5 4     ♦65      ♣9 8 7
Note, Cue bids are normally the Ace in the suit bid.

Simply bid 2NT (If that means a good raise to 3♥  or better); alternatively, bid 4♥ directly.  You do not have a singleton or void

4 losers, a tremendous hand, jump to 3♠; if Partner just bids 4♥  make one final slam try with 5♣  (Not 4♠, you have already shown a spade control).  Alternatively, there is nowt wrong with Blackwood, because, all you want to know about is Aces.

Bid 4♣ .  Partner will probably sign off in 4♥  when you should bid 5♦ denying a spade control. Partner will then realise how important a singleton spade is: e.g. 
♠7   ♥K J 6 5 4    ♦6 5     ♣ A K 10 9 7,  when they can bid 6♥ .  However, with
♠ 7 5    ♥ K J 6 5 4     ♦ 6      ♣  A K 10 9 7, they should just bid 5♥ . 

Prefer a bid of 3♦  to show a strong hand, and a SOURCE OF TRICKS. This jump bid, will either be a good diamond suit and support for the opening bid (Hearts), or a self-sufficient suit, that knows what it is doing.

Very difficult hand – Blackwood is no good; 1 Ace response leaves you not knowing which of King of hearts or Ace of clubs Partner holds. So, I prefer 3♦  and over 3♥ , (an expected weak bid), a jump to 5♣ , again an unnecessary jump to show a void club (questionable, I hear you say; so be it).

what do we bid on this?   Over 1♥ , I suggest we could use 5♣  to show a void, Otherwise, just bid 2♦ or 2 NT (Showing a good raise to 3 or more), the last 2 bids are equally acceptable. BUT not 3♦  which would show a better suit than A 10 9 8 5.

PLEASE UNDERSTAND, this is just as much for information (and my ideas, not from a textbook), as opposed to an exercise for you to learn.  SPLINTERS ARE FUN!