I will start from the last which is also the more difficult.
It's a difficult puzzle so we are going to explain it step by step.The first thing we must do is determining the draw positions.That is easier than sound but we need to think hypothetically.Let's assume black has the move.Can he draws?
Clearly when white's king plays to g5 if black king plays to e5(related square) it's a draw.We will call it Drawing Position 1(dp1).From dp1 we can easily find the correct move for white.
In the new position dp1 is no longer possible because of the pawn at f4 but what are the new drawing positions for black?
Again hypothetically speaking , what would happen if white played 3.Kg5?
Let's see it:
So , with white king at g5 and black king at e6 with white to move is again draw(dp2)
With the kings at opposite sides we have one more drawing position.
Let' s call it dp3.
We now have to find how white can win.White obviously have to penetrate and force black abandon the defense of the pawn but white has an advantage , an extra tempo from f4-pawn.In the following positions if black has the move loses f7 and if white has the move he can use his extra pawn to force black to move.
The above are white's winning positions.If we examine them carefully we will realise that white wins if his king reaches either e7 or g7.For this position these are the Critical Winning Squares.
Now we have the winning positions and we also have black's drawing positions.All we have to do is create one of the 2 winning positions avoiding black's drawing position.Let's see it:
I will start to explain the puzzles for those of you that interested.