White to move. Is this a draw or win for white? How should white proceed?
1.Ke3 Kf5 2.Kf3 Kg5 3.Ke4 Kg6 4.Kf4 Kh5 5.Kf5 Kh6 6.Kg4 Wins
You have to start with the recognition that white has to win the black h-pawn. If white tries exchanging for the h-pawn, he will be left with a rook's pawn and with a forced draw since the black king will beat white's to the corner.
Next, you have to notice that 1.Kf3 allows black to take the direct opposition from f5, and can match any move the white king makes after that keeping the white king off of the 4th rank forever.
Then you have to notice that moving backwards allows the black king to take over the fourth rank: 1.Ke2 Kf4 2.Kf2 Ke4 3.Ke2 Kf4=.
This leaves only one move to analyze.