Puppet stayman is a great convention, I highly recommend learning it. It does two things
1. Its main role - asks about 5 card majors. This is really useful when you have a type of hand that might play better in a 5-3 major fit than 3NT, for example
I would be delighted to play in 4♠ instead of 3NT with the 2 small doubletons. Even something more balanced, such as this, qualifies
Again 4♠ might be a fine contract here in a 5-3 fit with your small doubleton heart.
You also might have a 4 card major and a 3 card major to use it for example,
Here you are looking for either a 5-3 spade fit or a 4-4 heart fit. I will talk just below about how to find a 4-4 fit using puppet.
2. Puppet stayman has another role, to ask about 4 card majors. There are a couple reasons for that
a) The example just above is a classic case where you want to know about 5 or 4 cards.
b) Experts are using it more and more often as a substitute for regular stayman when they only are interested in one 4 card major. Let me show you a couple of examples to convince you.
On this bidding, the 1NT bidder said "No I don't have a 5 card major, by bidding 3♦. Responder then bid 3♥, saying - "I have 4 spades". The 1NT opener then bid 3NT denying 4 spades. It is unknown to the defence whether declarer has a 4 card heart suit or not - at the expert level that information is significant, for example the opponents don't know whether a heart lead is a great idea or if it is leading into declarer's heart suit!
Compare that with using Normal stayman which is more revealing, the auction would go like this
On this auction we have advertised to the opponents that declarer has 4 hearts - that might be information that helps them beat the contract either by not leading it, or by knowing something during the play that makes a difference!
What are the responses to puppet stayman
I have sort of clarified them above in the examples, but to lay them out
After a 1NT opening, 3♣ is Puppet stayman.
- 3♦ = no 5 card major
- 3♥ = 5 card hearts
- 3♠ = 5 card spades
After 1NT 3♣ 3♦ - responder can ask about 4 card majors by bidding the major they DONT have, so for example on this hand that I gave a moment ago, responder has shown 4 spades by the bid of 3♥.
Recommendation
Overall I strongly recommend playing Puppet stayman. It is a flexible tool that you can ask about 5 and/or 4 card majors, which often might be your best contract. A closing remark - if you have a 4-3-3-3, just bid 3NT rather than investigate a major game (4♥ or 4♠).
Read next: Find a Major Fit After 1NT: Stayman, Smolen, Puppet, Texas · Stayman Convention · Smolen Convention: Show 5-4 Majors After Stayman · Garbage stayman: Stayman with weak hands