When is an extra pawn enough to win?


Well I just had a quick look, I'm probably wrong :(
I suggest push immediatly, 1 b4.
Now if Rxb4 2 Rxb4 Rxb4 3 Ra8+ and the Knight fork can't be avoided.
If he doesn't take, push b5.
Also, more generally, try to keep in mind that this pawn has to be adressed all the time by your opponent. Try to find ways to create weaknesses elsewhere on the board, maybe even giving up the pawn at an opportune moment.
But, rather wait for stronger players comments... :)

In that position, I think White has a small advantage, but the position is extremely difficult to win, if it's even winnable. Black's going to play ...e5 at some point to win back the pawn, and White must always think about that possibility. In the meantime, the only thing for White to do is to expand on the kingside. 1. h4 looks very good to this end. Black will have difficulty responding to White's k-side advance. Normally, the side with the advantage would try to avoid a 4 vs. 3 endgame, and White is actively striving for one, but here, it seems to offer White the best winning chances.
rooperi noticed a pretty nice tactical shot that makes the immediate b4 possible. It also has the virtue of chasing the knight away. After that, you can either push again or move the a-rook behind the pawn too. To be honest, I haven't gotten into too many of these types of positions in the past, so I'm not exactly an expert on the topic.
I don't know if you've heard of this before, but I remember reading from somewhere that endgames with rooks and queens are the hardest to win, even if you're up a pawn (a rook and pawn vs rook often leads to a Philidor Position for example) while pure pawn endgames are the easiest to win when up at least a pawn. Personally, I hate it when knights are on the board in the endgame since calculations become much more complicated (how the heck are you supposed to see those forks when you've only got seconds to move?). I think it's a good idea to practice with someone (or with an engine). Play this position out again with Fritz or a good friend or mentor and see whether you can win it on the second try or the third try.
Generally, N & P endings with a pawn advantage are quite winnable for the side with the advantage, and R & P endings with a pawn disadvantage are quite drawable for the side with the disadvantage. So, while keeping in mind the tactics of any given position (i.e. don't hang anything), you generally want to activate your king, advance your pawn when safe to do so, and trade the rooks while keeping the knights (at least until the rooks are gone). Essentially, you want to avoid pawn exchanges and get the rooks off the board; they're the source of most of black's drawing possibilities. Black will want to keep rooks on, so you'll have to combine threats (which will revolve around advancing the passed pawn) with offers to exchange, i.e. black doesn't want to exchange rooks, but you have to make it so the alternatives are worse. The R & N ending is tough to win; the R & P ending is REALLY tough to win; the K & P and N & P endings are winnable. To win the R & N ending a pawn up, you generally need serious pawn weakness in your opponent's pawn structure. Not the case here (though it might be provoked). First 2 orders of business - activate the king & try to get the rooks off.

Some really good comments here. I'm having real trouble with my endgames. No matter how much I try I always seem to end up throwing games away when I am up a pawn because I feel nervous about my advantage and throwing it away! It's nice to hear some comments about general strategy for the different types of endgame. Thanks guys.