How do I use the Stayman convention in bridge?

Stayman is a bridge convention used to find a 4-4 trump fit in a major suit after the 1NT opening bid. It can also be modified for use after an opening 2NT, 3NT (strong) or a 1NT overcall. While the convention is named after the person who first wrote about it, Samuel Stayman, it was actually invented by J.C.H. Marx, British bridge player in 1939 (who published it only in 1946), and apparently independently by Stayman's partner George Rapee in 1945.