Pawn endgames
Draw the square of the pawn: one side runs straight from the pawn to its promotion square, the other sides complete it towards the defending king. If the pawn runs alone and that king can step into the square on his move, he catches it. Otherwise, do not chase — push your own pawn.
Two kings facing each other on a file or a rank, a single square between them: the side that does NOT have the move has the opposition, and the other must step aside. With your king in front of your pawn and his still in front of you (not a rook pawn), having it is enough to win. With your king beside your pawn or behind it, it is not always enough.
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The idea
The king does everything: opposition, key squares, the square. From the simplest rule to the fine manoeuvres, in the order you learn them.