How do you beat a person in chess in 4 moves?

Answer 1

One can't really answer this question. There are several good moves when your opponent first move is e2-e4, e.g. e7-e5 or e7-r6 or c7-c5. None of them will bring you victory by themselves you still have to play better than your opponent.

Answer 2

There is more than one way to defeat a player in only 4 moves. The so called "4 move checkmate", also known as "Fools mate" or "Scholars mate", involves a quick mate on f7, using the moves e4 (or E3), Bc4, Qf3 (or h5) and then Qxf7# (or in some cases even Bxf7 is mate). An example is

e4 e5

Bc4 Nc6

Qh5 b6??

Qf7#