King and queen vs king
Force the enemy king to the edge, then deliver checkmate - no stalemate.
Queen-and-king versus lone king is a forced win, but it is surprisingly easy to accidentally stalemate. The key is to use the queen to shrink the enemy king's available squares step by step while constantly checking for stalemate.
The technique: use the queen to push the enemy king toward an edge or corner. Then bring your king close to help. Deliver checkmate once the enemy king is on the edge with your king supporting.
Never give the enemy king no moves when it is not in check - that is stalemate and a draw. Always leave at least one escape square until you are ready to deliver the final check.
Examples
Queen corrals the king toward the edge
White plays Qd4, a square that limits the Black king's moves. The queen does not need to check - corralling works better. The Black king on d3 is being herded toward an edge where checkmate is possible. Notice White avoids Qe3, which would stalemate Black immediately.
Checkmate - king trapped on the back rank
White plays Qa6 - checkmate. The Black king on a8 is in check from the queen and has no escape: b8 is covered by the king on c7, and a7 is controlled by the queen on a6. This is the classic queen-and-king checkmate pattern: king on the edge, queen one square away with your own king nearby.
Key terms
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