How do I win this position
The free Basic Endgames course on Chessable covers it early on. I found the beginning of the course a bit confusing, but then it becomes simpler.
Whose move is it?
For king-and-pawn endgames, the general idea is to place your king in opposition against the enemy king (as depicted on your board), which forces the enemy king to move laterally. You advance diagonally, and repeat. Then you walk your pawn down the board, queen, and then go for checkmate.
If you are Black, you want to take the opposition, and then continually retake the opposition as White's king moves laterally. Run out the 50-move clock and claim a stalemate.
What do you mean by the 50-move clock, exactly? I would have thought the game would end more quickly by threefold repetition. Thanks for the summary in any case, I'll make a note of that.
This is a mutual zugzwang position: The side which has the move, has a problem.
If it is white to move, it is a draw- else white wins by placing the king TWO rows ahead of the pawn, and this is the generic rule to win such endings.
The diagram you have attached is with Black to play, so white wins by placing the king at e4 or g4 on the next move.