user7002: The tablebase suggests it's a win for White, but I struggle to beat my phone. Black's rook seems to always be able to harass the white king to stop white make any progress.
What's the technique to win this endgame?
[fen "8/8/6k1/6r1/8/8/6PP/5RK1 w - - 1 61"]


user13147: I remember drawing a rook and two pawns vs. rook position with g- and h- pawns. I was the losing side. Basically, 1) prevent king mobility, 2) win the rook pawn and 3) play the first rank defense on the g-pawn.

In rook endings, there are many positions where two pawns are not enough to win. Only opposite-coloured bishop endings present a higher drawish trend.
Excerpt From: "100 Endgames You Must Know: Vital Lessons for Every Chess Player Improved and Expanded" by Jesus de la Villa.

But what if the opponent plays accurately, and doesn't drop pawns?

The idea is as follows: set a blockade on the seventh rank by playing Rb7 and Kh7. If the king approaches, check him with your king on g6. If the rook attacks your king on h8, White has no time to move his King forward on the next move because of ...Kxg8.
To win, prevent the opponent from enacting this blockading strategy. Judging by the original poster's position, Black plays 1...Ra5 (or 1.Ra1 Rb5) and blockades.
Draw.
EDIT It is a draw only if the pawns are pushed without thought as another poster suggested. The strategy is to push slowly, one at a time and to avoid drawing positions as listed.

A two pawn advantage in most cases guarantees the win. But there are quite a few drawn positions, particularly when one of the pawns is a RP (as in OP).
Excerpt from Rook Endings. Smyslov and Levenfish.

This book is a great reference on such positions. There are eight pages devoted to it. Here is an excerpt:


user1485: As we can see from the other answers, there are two things you should avoid: 1) The pawns getting blockaded. 2) Your king getting cut off from the pawns.
It is not the only way to win, but as a matter of technique it is a good thing to advance the h-pawn before the g-pawn. In this way your king can use the g-pawn to hide both from checks from the side and checks form behind. But first use the rook to chase the opponent king as far back as possible.
Example:
[FEN "8/8/7k/R7/6PP/6K1/8/1r6 w - - 0 1"]
[Title "Rook endgame g+h"]

1. Ra6+ Kg7 2. h5 Rb3+ (2... Rg1+ 3. Kh4 Rh1+ 4. Kg5) 3. Kh4

The checks will stop and you can think of the next step.
[FEN "8/6k1/R7/7P/6PK/8/8/1r6 w - - 0 1"]
[Title "Rook endgame g+h"]

1. Ra7+ Kg8 (1... Kh6?? 2. g5#)  (1... Kf6 2. g5+ Kf5 3. Rf7+ Ke6 4. Rf6+ Ke7 5. h6) 2. h6 Rb5 3. g5 Rb1 4. Kh5

Here I would again chase the king away before advancing the h-pawn another step.
If the g-pawn is pinned there is no point in giving a check first.
[FEN "8/7k/R7/7P/1r4PK/8/8/8 w - - 0 1"]
[Title "Rook endgame g+h"]

1. h6 (1.Ra7+ Kh6) Rb1 (1... Rb5 2. g5 Rb1 3. Ra7+ Kg8 (3... Kg6 4. Rg7+ Kf5 5. h7))2. Kh5 Rb5+ (2... Rh1+ 3. Kg5) 3. g5

In this way you can advance slowly rank by rank. Towards the end black will have to defend passively to avoid mate at the back rank. Just for the fun of it I would try to end the game with a knight or bishop promotion like in my answer to this question.
[FEN "r6k/8/6PP/5RK1/8/8/8/8 w - - 0 1"]
[Title "Rook endgame g+h"]

1.Rf8+ Rxf8 2.g7+ Kh7 (2...Kg8 3.Kg6) 3.gxf8=N+!(3.gxf8=B!)(3.gxf8=Q??)(3.gxf8=R??)


7002: <p>The tablebase suggests it's a win for White, but I struggle to beat my phone. Black's rook seems to always be able to harass the white king to stop white make any progress.</p>

<p>What's the technique to win this endgame?</p>

<pre><code>[fen "8/8/6k1/6r1/8/8/6PP/5RK1 w - - 1 61"]
</code></pre>
 13147: <p>I remember drawing a rook and two pawns vs. rook position with g- and h- pawns. I was the losing side. Basically, 1) prevent king mobility, 2) win the rook pawn and 3) play the first rank defense on the g-pawn.</p>
<blockquote>
<p>In rook endings, there are many positions where two pawns are not enough to win. Only opposite-coloured bishop endings present a higher drawish trend.</p>
<p>Excerpt From: &quot;100 Endgames You Must Know: Vital Lessons for Every Chess Player Improved and Expanded&quot; by Jesus de la Villa.</p>
</blockquote>
<p>But what if the opponent plays accurately, and doesn't drop pawns?</p>
<p><img src="https://i.stack.imgur.com/nYKjO.jpg" alt="enter image description here" /></p>
<p>The idea is as follows: set a blockade on the seventh rank by playing Rb7 and Kh7. If the king approaches, check him with your king on g6. If the rook attacks your king on h8, White has no time to move his King forward on the next move because of ...Kxg8.</p>
<p>To win, prevent the opponent from enacting this blockading strategy. Judging by the original poster's position, Black plays 1...Ra5 (or 1.Ra1 Rb5) and blockades.</p>
<p>Draw.</p>
<p><strong>EDIT</strong> It is a draw only if the pawns are pushed without thought as another poster suggested. The strategy is to push slowly, one at a time and to avoid drawing positions as listed.</p>
<blockquote>
<p>A two pawn advantage in most cases guarantees the win. But there are quite a few drawn positions, particularly when one of the pawns is a RP (as in OP).</p>
<p>Excerpt from Rook Endings. Smyslov and Levenfish.</p>
</blockquote>
<p>This book is a great reference on such positions. There are eight pages devoted to it. Here is an excerpt:</p>
<p><a href="https://i.stack.imgur.com/z3qmC.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/z3qmC.jpg" alt="enter image description here" /></a></p>
 1485: <p>As we can see from the other answers, there are two things you should avoid: 1) The pawns getting blockaded. 2) Your king getting cut off from the pawns.</p>

<p>It is not the only way to win, but as a matter of technique it is a good thing to advance the <code>h</code>-pawn before the <code>g</code>-pawn. In this way your king can use the <code>g</code>-pawn to hide both from checks from the side and checks form behind. But first use the rook to chase the opponent king as far back as possible.</p>

<p>Example:</p>

<pre><code>[FEN "8/8/7k/R7/6PP/6K1/8/1r6 w - - 0 1"]
[Title "Rook endgame g+h"]

1. Ra6+ Kg7 2. h5 Rb3+ (2... Rg1+ 3. Kh4 Rh1+ 4. Kg5) 3. Kh4
</code></pre>

<p>The checks will stop and you can think of the next step.</p>

<pre><code>[FEN "8/6k1/R7/7P/6PK/8/8/1r6 w - - 0 1"]
[Title "Rook endgame g+h"]

1. Ra7+ Kg8 (1... Kh6?? 2. g5#)  (1... Kf6 2. g5+ Kf5 3. Rf7+ Ke6 4. Rf6+ Ke7 5. h6) 2. h6 Rb5 3. g5 Rb1 4. Kh5
</code></pre>

<p>Here I would again chase the king away before advancing the <code>h</code>-pawn another step.</p>

<p>If the <code>g</code>-pawn is pinned there is no point in giving a check first.</p>

<pre><code>[FEN "8/7k/R7/7P/1r4PK/8/8/8 w - - 0 1"]
[Title "Rook endgame g+h"]

1. h6 (1.Ra7+ Kh6) Rb1 (1... Rb5 2. g5 Rb1 3. Ra7+ Kg8 (3... Kg6 4. Rg7+ Kf5 5. h7))2. Kh5 Rb5+ (2... Rh1+ 3. Kg5) 3. g5
</code></pre>

<p>In this way you can advance slowly rank by rank. Towards the end black will have to defend passively to avoid mate at the back rank. Just for the fun of it I would try to end the game with a knight or bishop promotion like in my answer to <a href="https://chess.stackexchange.com/questions/730/why-would-one-promote-a-pawn-to-a-knight/4000#4000">this question</a>.</p>

<pre><code>[FEN "r6k/8/6PP/5RK1/8/8/8/8 w - - 0 1"]
[Title "Rook endgame g+h"]

1.Rf8+ Rxf8 2.g7+ Kh7 (2...Kg8 3.Kg6) 3.gxf8=N+!(3.gxf8=B!)(3.gxf8=Q??)(3.gxf8=R??)
</code></pre>
