Stayman

Stayman is a convention (not natural) that is mainly used to find an 8 Card Fit in a Major when partner opens 1NT (12-14).

Bid 2C to ask whether Opener has a 4 Card Major.

If 1NT Opener has a 4 Card Major then she bids that Major at 2 level - 2H or 2S.

If she has BOTH 4 Spades and 4 Hearts, then bids she 2H.

If she has no 4 Card Major, then she bids 2D.

You should really have a game-going hand of 11 plus points to bid 2C Stayman. If you have both a 5 Card and a 4 Card Major you can bid 2C with fewer points.

Responder must have a plan for whichever answer (2H/2S/2D) is given and bid accordingly after Opener replies. Opener must not bid again.

If you have 13 points and a flat 4, 3, 3, 3 shape, it may be better to jump to 3NT even if the 4 is a Major.

If opposition Overcalls or Doubles the Opening Bid then the Stayman convention is off.

IMPROVERS 

Stayman is also used after a 2NT (20-22)Opening. Bid 3C (Stayman, asking for Majors).

Stayman can also be used after 1NT OVERCALL (16-18) if agreed with partner.

1D - 1NT - PASS - 2C (asking for a 4 Card Major)

You can use Stayman without a game-going hand (11+ HCP), to put partnership into best contract. This relies on the 1NT opener sticking to the rules and not bidding again (unless asked).

PHONEY STAYMAN - This is a weakness takeout into Clubs.

1NT - PASS - 2C - PASS - 2H/2S/2D - PASS 3C 

EXTENDED STAYMAN - when you have 5 Card  Majors and want to find out if Opener has 3 of a Major.

1NT - PASS - 2C (have you got a 4 card major?) - PASS - 2D (no) - PASS - 3D (have you got a 3 card major?)-PASS - 3H/3S (yes 3xH / yes 3xS)