user7387: 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?

user2429: 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+

7387: <p>I read from <a href="http://www.chess-insights.com/rook-vs-single-pawn.html" rel="nofollow">this website</a> (example 2) that you can win the game in the following situation:</p>

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

<p>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.</p>

<p>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.</p>

<p>How can this game play out?</p>
 2429: <p>You don't necessarily have to intrude with your king to the queening square. 
You really need 3 things - </p>

<ol>
<li>Get the king close to the pawn</li>
<li>Control the pawn's advancing square with both pieces </li>
<li>Capture the pawn</li>
</ol>

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

<p>So, for e.g. 
1... Ke5
2. f6 Rf4
3. Kg6 Rxf6+</p>
