Pawn endgames
The rule of the square: draw a square whose diagonal runs from the pawn to its promotion square — if the defending king can step inside it on its turn, it catches the pawn; otherwise the pawn queens. Count both sides' moves before you race.
Zugzwang and the opposition: when every move worsens the position, the side to move gives way. Take the opposition (kings facing off with one square between them, the opponent to move) to force the enemy king aside and clear the path for your king and then your pawn.
Exercises built from YOUR games (solved, missed) are part of ChessPivot Plus. Discover ChessPivot Plus
The idea
The rule of the square: draw a square whose diagonal runs from the pawn to its promotion square — if the defending king can step inside it on its turn, it catches the pawn. Otherwise the pawn queens. Before racing, count both sides' moves and check the opposition: an active king in front of its pawns is often worth more than an extra pawn.