King and rook against a lone king is a guaranteed win, but unlike the ladder mate it can't be done by the rook alone: the rook shrinks the box the enemy king lives in, and your own king walks up to take away the squares the rook can't cover. Every rook endgame you ever win funnels into this exact technique.
The finishing position to memorize: the two kings stand directly facing each other, one square apart, and the rook checks along the edge rank. The enemy king can't advance (your king blocks every square) and can't stay (the rook covers the whole rank). Drive the king to the edge, get the kings face to face, then deliver.
Kings face to face with the black king on the edge. The rook is ready to close the box.
The kings are in position. Close the box.