How to Win King vs Pawn in this Situation I read from this website (example 2) that you can win the game in the following situation:

[Title "Black to move - Black's POV"]
[fen "8/8/8/5PK1/1r1k4/8/8/8 b - - 0 59"]


I play as black. I want to keep the rook and king to win the game, and prevent him from queening. I can't let my rook be captured.

But he doesn't finish the game. He just says "And in this position you'll always be able to win the pawn and the game." But I don't see how I can intrude with my king to the queening square.

How can this game play out?
You don't necessarily have to intrude with your king to the queening square. 
You really need 3 things - 


Get the king close to the pawn
Control the pawn's advancing square with both pieces 
Capture the pawn


So, in this case, 
Ke5 followed by Rf4 will achieve steps 1 and 2. Then you can capture the pawn and win. 

So, for e.g. 
1... Ke5
2. f6 Rf4
3. Kg6 Rxf6+