Since you can't control your opponent's choices in chess, there is, of course, no such thing as a formula for a simple, quick and certain checkmate. A checkmate is possible in three moves, based on likely actions of an opponent. In tournaments, this checkmate formula quickly weeds out the most inexperienced opponents, allowing you and the other serious contenders to save your mental energy for the task of defeating each other.
Try to play as white. The rules for a traditional game of chess require the player controlling the white pieces go first, and this move is more likely to be successful if that player is you. If you are forced to play black (tournaments will most likely require that players flip a coin for this coveted position), you may still be able to pull off the three-move checkmate, but there's a greater chance that the starting player will make a move that will prevent you from even starting this move.
Move your pawn from E-2 (fourth from the left; the chess board graph uses letters across and numbers down) to its required first-move position, two squares forward (E-4). If you are lucky, your opponent will counter your pawn by moving one of his into a position where it can attack you, requiring you to attack his or leaving your pawn open for attack, either removing your pawn or moving it from its intended target. If he moves his F-7 pawn to F-5 in order to do this, proceed with the checkmate.
Pick up your queen and move her two spaces diagonally to F-3. With luck, your opponent will respond by starting to move another pawn into place to defend against your queen by attacking diagonally. If she moves her second pawn into G-5, a checkmate will become available to you the instant she removes her hand from the piece (making the move officially finished, according to tournament rules).
Take your queen and move her diagonally forward another three spaces, positioning her at H-5. From this spot, she is now threatening the king. Since the king is still mostly surrounded by other black chess pieces and can only move deeper into the queen's path, the match is now at checkmate, and you have won the game.
This move can also be used to defeat some simpler computer chess programs, so you can use it to test a game for quality.
Your queen will be unprotected.