The pawn moves straight forward one square at a time, and only forward. On its very first move it may go two squares. It captures differently from how it moves: one square diagonally forward. It can never move backwards.
In these puzzles you walk a pawn up the board to the goal square. The wall pawns are rocks you can't take, and the pawn can't step sideways, so when a rock is straight ahead the only way on is to capture one of the black knights diagonally.
Tip: a pawn that is blocked straight ahead is stuck unless it can capture. Before you move, look at what is diagonally in front of you.