Have you ever reached the end of a game with only the two kings and
one of your rooks left?
Well, here's a sure-fire way to achieve mate from exactly that situation:
check your opponent's king with your rook,
forcing him to choose a side in which to retreat.
If the king ever gets too close, zip your rook to the other side of the board,
but keep that king fenced in. Next, position your king on the square directly
across the fence from your opponent's king.
Once the kings are facing one another, move your rook one square away from your king,
checking her king. It must retreat.
Repeat this process until you've backed it against a wall.
Then, check one more time for mate.