Puppet Stayman uses a 3♣ response to enquire about opener's major-suit holdings. Opener rebids 3♥/♠ to show a five-card major suit, and 3♦ to show one or both four-card majors. With neither a four- or five-card major, opener rebids 3NT.
Over opener's 3♦ rebid, if responder also has a 4-card major he/she bids the other [hence Puppet] to ensure the opener plays the contract. If responder has both four-card majors, he/she bids 4♣ with slam interest, 4♦ to sign off in opener's major.
Note that responder should bid 3♣ with three-card holdings in either major, to cater for opener having a five-card major with 4-major being the best contract.
Breaking Transfers
We're following Article 8 in Andrew Robson's Modern Bidding Developments. The essence of this is that where responder bids either 3♦/♥ as a transfer, opener breaks the transfer with at least three-card support.
If the auction starts 2NT - 3♦:
Over the 3NT and 4♣ rebids, responder can now bid 4♦ as a re-transfer back to 4♥ to right-side the contract.
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