Endgame Crash Course: Basic Checkmates
The most basic checkmate of all (save for Queen and Rook, which is practically the same) is the checkmate with two rooks - the King does not even need to participate in the Kinghunt:
Checkmate with a Queen is also not too taxing - the method here is not usually the quickest or the most efficient, but again, is the most methodical and easiest to learn:
Here is the Rook checkmate. The sequence here is slightly more complicated, since the King's involvement is necessary, both to drive the opposing King back, and for checkmate: