The king and queen vs. king checkmate is one of the most basic endgames in chess. Knowledge of this and other "overkill" endgames is crucial to improving your chess. After all, it isn't enough to gain a winning position -- you need to be able to checkmate your opponent's king.
From the position above, White's first step should be to limit the Black king's area of movement. The queen is ideal at sealing the king into a small area.
White can begin to limit Black's king by playing 1. Qe5.
