I'll give you some ideas every chess player can use when playing rook endgames.
In this position Black could win if the rook could move away from the a-file without losing the pawn.
There are three ways this could be possible, but White can prevent them all from happening.
1. If Black could protect the a-2 pawn with his king, the rook could move away.How can this be prevented by White?. As soon as the black king comes to b3, White will start checking the king from behind with the rook. The black king has no shelter and as it leaves the-b3 square, the white rook can return to the a-file.
2. Play the rook away with check (without being captured), then promote the pawn next move. This would be possible if the White king isn't on the second rank. If it was on g4, then Rg1+ would end in promoting the pawn. You can prevent this by keeping your king on g2 (or h2).
3. Move the rook away with a possible skewer. This could be possible if the white king would be on the second rank, but not on g2 or h2. Had the white king been on f2 (or e2, d2 ) then 1...Rh1 would win the game. After 2.Rxa2 the skewer 2....Rh2+ would win the white rook.
You need to remember this:
If you're defending this position, it's a good thing to have your rook behind the black pawn. Now the black rook can't move away without you capturing the pawn.
You'll have to keep your king on the drawing squares (g2 or h2). This way the rook can't escape with a check or a skewer.
If the black king threatens to help the pawn, you can force it to leave by checking it from behind.
Idea 1: Rook behind the passed pawn.
Idea 2: King in the safe zone.
White to play will win. How does he do this?
It's done by cutting off the black king.
The black king can no longer support the pawn. The pawn isn't going to reach the other side now.
After 1....c3; you have two ways to stop it.
variation 1: 2.Rg3, c2; 3.Rc3, c1Q; 4.Rxc1, and the pawn is gone.
variation 2: 2. Kg7, c2; 3.Rg1, Kd4; 4.Rc1, winning the pawn next move.
Idea 3: cut off the king.
This may be a little more difficult. White to move saves himself.
It may be useful to know this stalemate trick.
1. Ra7+ (chase the king away), Kg8;
White voluntarily sets his rook up for an x-ray attack.
3.Kg6, Rxa5 stalemate;
Have you seen this motif before? If not, it's worth remembering.
Idea 4: Look for common stalemates.
Even grandmasters may overlook this stalemate resource.
Here Black could have taken a pawn with 1....Rxh5.
This would have saved his game because of the stalemate trick.
2.Ra5+, Kb4; 3.Rxh5 stalemate.
Unfortunately, Morozevitch played something else (Kb4) and lost the game.
When kings are far away, two connected pawns on the sixth rank will beat a rook.
Black can't stop the pawns. 1...Re8; 2. f7 and one of the pawns will queen. The best black can hope for is to draw a queen vs rook ending (which isn't always easy to win).
Idea 5: Two connected pawns on the sixth rank usually beat a rook.
Now take a look at the next position...
If White has the move, you now know what's going to happen.... (don't you?).
Sure! White plays 1.f6, getting the pawns to the sixth rank and winning.
Back to the starting position once more.
Now if Black has the first move, and you're playing as Black, what would you do?
Right! Prevent the pawns from reaching the sixth rank.
In this position after 1....Rg3!; the pawns can't advance without being captured. White will play 2. Kd2, keeping the pawns as they are.
Now you can force the pawns to move with 2....Rg5;
Here 3.Ke3 is too slow (3...Rxf5; 4. Ke4, Rg5; winning the pawns).
Unfortunately for White, the pawn moves aren't good either.
3.f6 fails to 3....Rxg6; and winning both pawns.
The last possibility is 3.g7, Rxg7; 4.Ke3 and it looks good, but actually fails to 4...Rg4 ( the king is cut off and White loses his last pawn);
Idea 6: prevent connected pawns from reaching the sixth rank.