Cornering and avoiding stalemate
This article is intended for relatively new players and maybe a few intermediate players as well. The goal here is to emphasize checkmate when you have a one-piece advantage over your opponent, who only has their king remaining. This article will cover king and queen vs. king, king and rook vs. king, and king and pawn vs. king situations.
King and Queen vs. King:
Of the three situations described above, this is by far the easiest. Since the queen can move laterally and diagonally, the enemy king can never put himself near her. Your goal is to box the black king into the corner, but always leave at least TWO possible spaces for him to move until you're ready to go in for the kill. Otherwise, it is a stalemate, and all your effort will amount to nothing, really.
Do NOT allow either of these situations to happen:
King and Rook vs. King:
This situation is similar to the last, but slightly more difficult. You still want to box the enemy king in, but you have to line him up right with your king in order to set up checkmate.
King and Pawn vs. King:
This is pretty common in endgames, and if the disadvantaged player is exceptionally clever, stalemate is a good possibility. Below, white's goal is to promote his pawn to a queen or rook in order to finish out with one of the above checkmates. Black's intention is to prevent that. Notice that if white cannot control the end zone before black gets there, then the cause is essentially lost.
What can white do to prevent this situation? You try and figure it out.
Keep in mind that this is far less likely to work when the advancing pawn is on the a or h file.