A rook beats a lone pawn when your king can get in front of it, or when the enemy king is too far away to help it. If the enemy king is close, use your rook to cut it off along a rank or a file, so it can't reach its pawn. A rook behind the pawn stops it all the way down the board. Then bring your king over and win the pawn. With the pawn far up the board and its king next to it, it is often only a draw.
Every move is checked with an endgame tablebase, which knows the exact result of every position with up to seven pieces. The computer defends perfectly, and if a move throws the result away, the trainer stops and shows you a better one.
