King and queen versus a lone king is the most common basic checkmate — and the one beginners most often stalemate by accident.
Use the queen a knight's-move away from the enemy king to shrink its 'box' of available squares, driving it toward the edge of the board. Keep that knight's-move distance and the enemy king is forced backward without ever being stalemated in the open.
The queen alone cannot deliver mate — you must walk your own king up to support it. Drive the enemy king to an edge with the queen, then march your king close.
With the enemy king on the edge and your king two squares away supporting, the queen delivers mate on the edge. Avoid stalemate: before each queen move, make sure the enemy king still has a legal square until the moment of mate.
Practice this until it's automatic — it appears constantly in real games.