In general the order of importance is (form highest to lowest)
1) Rook activity
2) King activity
3) Material
In particular if you can create a R+K+P trio where the pawn is on the opponent's half of the board, then that can be worth giving up a lot of material. The classical example is this game:
http://www.chessgames.com/perl/chessgame?gid=1102104
Other simple ideas can be derived from this. For example, if rook activity is important as I said, then what should white play in the position below?
(I only wanted the first move to be part of the puzzle, you can just use hints after the first move if you want)
Here's another typical example
(I only wanted the first move to be part of the puzzle, you can just use hints after the first move if you want)
Another typical decision
(I only wanted the first move to be part of the puzzle, you can just use hints after the first move if you want)
And in general, be ready for mutual attacks and threats, sort of like when players castle on opposite sides. When you're winning a king and rook endgame (or trying to draw) often both players infiltrate, both captures pawns creating passers for their side, and both rush those passers down the board and a lot will depend on efficient king and rook placement to see whose pawns queen first.
Here's a recent blitz game I screwed up (but won in the end anyway heh)
My big weakness is endgames where there are rooks, pawns & kings. Is there any general principles that apply in endgames with rooks (like there are opening principles, middle game principles)? Is there any good texts or videos on youtube that you can recommend for me to study?