It is possible to checkmate an opponent in 3 moves or even in 2, although such attempts are unlikely to succeed against any but the most foolhardy beginner, hence "Fool's Mate", which is the generally accepted name for short mates of this type. Here are two examples, given in standard algebraic notation:
1. f3 e5
2. g4 Qh4# (shortest possible mate in chess)
or
1.e4 g5
2.d4 f6
3.Qh5#
There are of course several other variants on these, but I wouldn't expect much success with any of these.