Some pawn structures are interesting to remember. For instance the following. Here the connected pawn is poisonous, that is, if black king captures it, the other pawn cannot be caught. Therefore, this formation defends itself without the king. Just let it stay in place, walk slowly up with your king and then start to advance the connected pawns. They are unstoppable.
Two pawns one file apart also defends themselves. If the king goes for one, the other escapes.
When it comes to tactics involving passed pawns or transition to an endgame ... if you can reach one advantagous formation like these, you can sacrifice your pieces if you like with confidence. It is not magic, just tactic.