Instructions
Look to see whether either king is in check. If a king is in check, a stalemate cannot occur.
Check to see if neither player is able to make a legal move. This usually happens when there are very few pieces left on the board.
Determine whether moving any pieces by one player would allow the opponent to capture your king. A piece cannot move if by moving the piece, the king can be captured--thus ending the game.
Find out whether by moving your king, it can be captured. If your king can be captured if it's moved in any position, the king cannot move.
Keep in mind that only the player who's turn it is has to be unable to move any piece in any direction in order for a stalemate to occur. If the other player can move, that does not matter.
Understand that there is a difference between a stalemate and a checkmate. A checkmate occurs after you have moved one of your pieces, putting your opponent's king at risk of being captured on the next move if he doesn't do anything to stop the capture. A stalemate occurs when it is someone's turn and that player is not under a check and in which he cannot move any of his pieces legally.