King + Pawn vs. King endgames
Endgames are tricky, even grandmasters struggle with them. Here's just some notions about King + Pawn situation.
In such a position, you should search the "opposition".
Direct Opposition is a position in which the kings are on the same rank or file and they are separated by one square. In such a situation, the player not having to move is said to "have the opposition" and the player who have to move can’t make progress with their king, potentially allowing the opposing king access to important squares (such as the promotion square).
If you want to hold a draw against a pawn, you have to take opposition with your opponent king and stay on the same file as the pawn whenever you can.