Hello,

I was loooking at this webpage, and could not find a way to win with white.

Can you find a way to win? http://www.chessvideos.tv/endgame-training/king-and-pawn-checkmate.php

Every legal move for white wins -- hope that helps

But seriously, get your king to a6 and you're good -- many beginners fall into stalemate and cannot promote the knight pawn, but this is a win.

If black to move it's easier.

Err, maybe not the best examples, but you get into stalemate when you swing the king towards the center of the board -- to avoid it go to the rook file... unless it's the 2nd diagram, then you can just do the standard bridge building.

Not close.  Any King move to the third rank is a draw: Black moves to keep the Opposition, and White has no spare Pawn move.

For the opening poster: The following position is standard in these endings:

The principle holds up on all files except the a and h (the Rook files) and with White's King on the 3rd, 4th, or 5th ranks.  The pawn can be directly behind the King or one square to either side (e.g. any adjacent square behind White's King).

If Black moves, the Opposition is quickly lost, and with it the game:

1 ... Ka6
2 Kc5 Kb7
3 Kb5!

And not 3 b4?? Kc7! drawing as below

3 ...  Ka7
4 Kc6 Ka1
5 Kb6 Kb1
6 b4 Ka1
7 b5 Kb1

I allowed Black the Opposition here, because it doesn't matter when White's King is on the sixth rank.  
 
8 Ka6 Ka1
9 b6 Kb1
10 b7

And White promotes.

If White were to move in the diagram, it would be a draw.

1 Kc4 Kc6!

Black keeps the Opposition until White pushes the Pawn.

1 b4 Kb6
2 b5 Kb7
3 Kc5 Kc7
4 b6+ Kb7
5 Kb5 Kb8!
6 Kc6 Kc1
7 b7+ Kb8
8 Kb6 stalemate

With that in mind, the winning move in the opening poster's diagram is:

1 b3!

With that move, White uses the extra tempo that the Pawn move gives in order to gain the Opposition and win as above.

Oh, you're right.  I didn't even think of moving the king to the 3rd rank, which of course would be a draw.

How about any reasonable move wins for white ;)

With white to move it is still a win of course.