Assault on the castled king
When your pieces aim en masse at the enemy castle, material stops mattering: what counts is how many attackers arrive and how many defenders remain. If the attackers win the count, there's almost always a sacrifice that breaks the wall open.
The typical levers: sacrificing a piece on h7 or g7 to tear off the castle's pawns, lifting a rook via the third rank (Re1-e3-h3, the “rook lift”), or pushing the f-pawn to f5-f6.
Once the king is out in the open, the golden rule is to give it no air: each check must draw it toward your pieces or away from its own. A king hunted in the open rarely gets home.
The guided example is one of the most famous games in history: Eduard Lasker vs George Thomas (London, 1912). A whole-queen sacrifice, and the black king walks across the board to its mate.
Practice the pattern
Several positions with the same pattern in different structures. You do each one twice: first following the arrows and, right after, without them.