Chess/The Endgame/Rook and Pawn Endings
Endgames where one side has a rook and the other a rook and one or more pawns, with no other pieces except the kings, is one of the most common in chess. Knowing the concepts of how these endgames work is essential to the intermediate to advanced player, and can result in many wins from otherwise drawn situations (or draws from otherwise lost situations).
Rook and pawn endings are very complex, and even professional players don't always execute them correctly. This module cannot provide a completely comprehensive guide of the subject, but aims to educate you to the most common, basic techniques.
Following is a list of different rook vs. rook scenarios. They assume that there are no other pieces on the board not indicated (except for kings). The goal in each for the attacking side is to promote a pawn, in which case the attacking side can then exchange rooks and execute a king-and-queen-versus-king checkmate.
Three or More Pawns and Rook vs. Rook 
This situation should always be a win for the side that has the pawns and is not terribly difficult to play (especially if at least two of the pawns are on adjacent files.). The defending player's rook cannot cover all pawns at once as they advance down the board.
Two Pawns and Rook vs. Rook 
This scenario usually results in a win for the player that's ahead, but in practice can be more challenging to execute. If the two pawns are connected, or on adjacent files, then the win is comparatively easy because one pawn can support another as they march down the board and the defending side cannot block one pawn with his king without getting checked.
When the pawns are separated, then things are less clear. If there is a large distance between pawns (two or more files), the attacking side may have trouble defending both at once and may opt to give up one pawn to transition into a more favourable (but harder) single pawn endgame.
It is also important to take into consideration how advanced the pawns are. If they are on the second-third rank, then queening will be inherently harder because of the distance they need to travel to reach (which results in more time for the defending player to blockade).
One Pawn and Rook vs. Rook 
Situations where one side has only a single pawn are the most complex of all rook and pawn endgames. Unlike the two above scenarios, they are not cut-and-dried, and there are more factors involved, such as the positions of both kings and rooks and the file the pawn is on.
As a general rule of thumb, if the defending side's king is a rank or more behind the pawn, then the pawn will queen because the attacking Rook can cut off the king from the action. (see Diagram 1). In this instance, white to play wins with 1. d6 Re8+ 2. Kd7 Rg8 3. Kc7 Rg7+ 4. d7! when black is out of checks and cannot defend the queening square.