Because rooks are usually kept in reserve during the opening and middlegame, they often avoid being traded off in mass exchanges, as can often happen with the minor pieces, and so rook endgames are the most common type of endgame. A well known chess idiom, often attributed to the late 19th/early 20th century grandmaster Siegbert Tarrasch, states that "All rook endings are drawn." This is rather tongue in cheek of course, as there are many possibilities for winning in rook endgames, but it is true that there are certain positions that are difficult to win even with an extra pawn.
As with other endgames, passed pawns are very important to winning in rook endgames. When you have a passed pawn, it's usually a good idea to put your rook behind it and protect it from the rear. Then you can push the pawn, and it will still be protected by your rook.
If it's your opponent who has the passed pawn, it might seem that the natural place for your own rook is in front of the pawn, to stop its progress. However, it's often better to get your rook behind the passed pawn, just as you would with your own passed pawn.
Unlike a bishop or knight, a rook has the ability to cut off the enemy king from the action, by creating an impassable barrier along a rank or file. This can be useful in both attack and defence.
Sometimes, in a rook and pawn endgame, one player may have to sacrifice their rook to prevent an enemy pawn from becoming a queen. Usually, this means losing the game, as the side with the rook will capture any remaining pawns and give checkmate. A rook is worth the same as five pawns, so if you lose your rook and do not get enough pawns in return, you may find it difficult to save the game. However, there are scenarios where the side with only a king and pawns can make a draw or even win. A king and a single pawn can often draw against a rook, if the enemy king is too far away to help.
In most cases, a rook can overpower two pawns, but if the two pawns are connected passed pawns (i.e. they stand side by side and have no enemy pawns ahead of them) on the sixth rank, then they can beat a rook without even needing the help of their own king.