White draws by moving his king diagonally to keep in touch with the opposing pawn and his own pawn. Black will have to move his king at some point to stop the white pawn queening which gives White enough time to stop the pawn.
The winning sequence is as follows:
1. Kg7! h4
2. Kf6 - continuing the diagonal movement to keep in touch with both pawns
2..Kb6 - Black now has to stop the white king from supporting the pawn on c6 and forcing promotion, when both pawns will promote with a draw.
3. Ke5! Kxc6 - Black must capture the white pawn, which allows the white king inside the square of the pawn,
4. Kf4 draw - as the white king can stop the pawn promoting
The winning sequence is as follows:
1. Kg7! h4
2. Kf6 - continuing the diagonal movement to keep in touch with both pawns
2..Kb6 - Black now has to stop the white king from supporting the pawn on c6 and forcing promotion, when both pawns will promote with a draw.
3. Ke5! Kxc6 - Black must capture the white pawn, which allows the white king inside the square of the pawn,
4. Kf4 draw - as the white king can stop the pawn promoting