The Four-Move Checkmate
This move will only be likely to succeed against a novice player as any opponent with experience on his side will be aware of this trick and quickly move to block you. Move the pawn in front of your king one or two squares forward (it doesn't matter which). Move the bishop on the king's side three diagonal squares in the direction of the pawn in front of your king. Move your queen diagonally two squares so that she is placed in front of the king's bishop's pawn. Now move your queen all the way forward and take the king's bishop's pawn on the opposite side. The king is now in check; he can take the queen, but this will leave him vulnerable to the bishop, creating checkmate.
The Three-Move Checkmate
This tactic is better performed as the white, as you will need to make the opening move of the game. Move the pawn in front of your king forward as you did in the four-move checkmate. After this move, you need your opponent to move his king's bishop's pawn forward one square. Move your queen diagonally three squares so she sits in the column of your king's knight. Now move your queen into the space in front of this pawn. This will leave her exposed to attack, but also leaves your opponent's king with nowhere to escape from the diagonal check from the queen. This forces checkmate.
The Two-Move Checkmate
Due to how short this sequence is, it depends heavily on mistakes made by your opponent, but if played correctly, it will deliver a quick and decisive victory. To play this sequence you must use the black pieces as this means you move second. Your opponent must move his king's bishop's pawn first forward one square. Next select your king's pawn and move him forward one or two squares as before. This leaves your queen open to move diagonally to the edge of the board, putting the king in check. From within this formation he should be unable to escape, forcing checkmate.
Defense Oriented Tactic
This sequence does not lead to a checkmate, but will leave your king in a strong defensive position to carry on into endgame and defeat your opponent. Playing as white, move your queen's pawn forward two squares. Now move your king's knight forward in its typical movement forward two and then either left or right, jumping over the pawn. Move the king's pawn one space forward. Now move your king's bishop diagonally forward two spaces into the queen's column. Now castle your king with your rook (a chess technique allowing you to swap certain pieces). This will leave your king in a nearly impenetrable position, allowing you greater tactical freedom of offense.