http://www.k4it.de/?topic=egtb&lang=en
The first diagram is a draw. Tablebases are great :)
Well, go to that link, and play your position out on there. At least you'll find the single move that lost it for you.
I thought it was amusing that the first move in the list of drawing moves in the first diagram for black is Rb1 :)
Pointers for general play:
1) Bring your king to the centre (obvious) possibly by threatening rook exchanges to help him there.
2) Once in the centre, there's the Cochrane defence. Keep the bishop pinned to the opponent's king while walking around, avoiding corners.
3) If that somehow crumbles, try the second-rank defence. Keep the rook on the second rank with your king, and be very careful, but it should be drawn.
4) Don't walk into corners (obvious).
Information courtesy of an article on this site (I forgot the link but remember the ideas), Basic Chess Endings and Wikipedia. Further reading: search for the Philidor, Lolli and Czen (Szen) positions.
Last night, I played a game over the board with one of my friends, and we got into a Rook vs. Bishop and Rook ending (I had the Rook).
The game went on for about 23 moves before I made my first move that I would consider a blunder. I accidentally headed to the corner controlled by his bishop, and was promptly mated.
I had never played in this ending before, which I think explains my poor play in it. Could anyone give me any pointers as how to more precisely play this ending? I know some bishop/rook vs. rook endings are actually won, but I have no idea if the position I showed was able to be drawn or not.