Puppet Stayman
Typically used to allow an opener to make a 2NT call on an otherwise balanced hand with a 5 card major suit and however many HCP you normally require for the bid (usually 20 to 21 nowadays.) The reason you want to be able to open this hand 2NT is that you don't want responder to pass a 1H or 1S opening unless he is totally devoid of useful values, yet the hand is too weak for a strong 2C opening.
The puppet Stayman sequence goes like this:
Opener Responder
2NT 3C (Puppet Stayman)
Opener now bids a 5 card major if he has one,
bids 3D with one or both 4 card majors,
or bids 3NT with 3 or fewer cards in each major.
Responder, if opener bids 3D, can sign off in 3NT, or if he has a four card major, shows it by bidding the *other* major (thus making sure that the strong hand will play the hand in the event of finding a fit) or, holding both major suits, bids 4C with slam interest, or 4D without.
You can follow these up with any slam seeking methods you want. It is worth noting that it is possible to play these methods in 1C forcing systems, after either a 1NT or a 2NT re-bid by opener.
There are many variations on this convention.