Okay, I blundered but what's the best move, dammit?

...Rf8, then ...Ne7 or ...Bf5, and you have everything defended, your opponent is down a piece, and you can start piling up on his pawns and grabbing them. There isn't much room for mistakes here, just try not to get your rook trapped by bishops early on.  Even if you do and have to exchange the rook for one of the bishops, you are much better off in the end.

I'm not sure...

1...Rf8 2. Rg1 and now if 2...Ne7 - it gets pretty unpleasant after 3. Bf5+ Kf7 and 4. Rg7+. 

I would stick to 1...Bf7. Of course black should win - but the position is still a bit tricky. One can't just play anything...

Actually, indeed, after playing around with Stockfish a bit, I can say that the position for white is much better than it looks, and it is actually very hard for black to get out of this attack, if white plays right. Attacking moves like Rg1 and Be5 for white are very dangerous, and black probably has to give some material back to survive. White also has the f-pawn marching idea...

I'll play some more with it tomorrow, but the more I look at it, the more it seems to me that white is actually very likely to win this game, if both players make the best moves.

Everybody can look at Stockfish...

But just for my curiosity - how does white answer 1...Bf7?

If 2. Rg1, then what after 2...Bxg6 3. Rxg6+ Kf8?

And lastly in this variation, if 4. Rg7 - what after 4...Re7?

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Now that I look at it, it seems that white does have 1...Bf7 2. Bf5! with a lasting initiative. 

Black does have an extra piece - but that piece is a knight, and it's fighting against a bishop pair that's already taking many squares from the black forces - and white also has an open g-file. 

I didn't see any clear way for black to come out of it. If the Nc8 moves, then the d6 square becomes usable for the black bishop, with ideas of pins etc. 

I don't think that white should already be winning, of course - but it certainly no longer looks like an easy win for black either.

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On the other hand, I'm not sure that I like 1...Rf8 2. Rg1! and we have no time for 2...Bf5...

Now 2...Kh8 3. Be5+! Nf6 and 4. h7- it looks like white gets what he wants - to pose the greatest amount of problems and tie up the black forces...

He's down a piece, but it isn't easy to fight against these three long-range pieces. 

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Having read IM Pfren below, I now put a bit of order in this post, which was a bit confused before. 

It seems that there's no easy way to get out of this passive situation and make something out of the extra piece.

I'm not sure if I like better the 1...Rf8 2. Rg1 Kh8 variation - or the 1...Bf7 2. Bf5! variation. 

Both are difficult to play - but on the other hand, I don't see how white wins this either. He IS down a piece. It could be a sort of dynamic equality - more comfortable for white for the time being, but stuff happens...

Unless the losing is easily spelled out, after I make a blunder I try to point every piece I have at his King or undefended pieces and launch and all-out attack.

In your case you're only down the exchange and a Pawn, you have to worry about your opponent's h-Pawn and your potential dark-square weakness.  He has two undefended Bishops as well as 3 of his 5 Pawns.  You don't have a lot to work with, but I'd consider moves like Nf6 attacking the e8-Bishop or Nf5 attacking the d4-Pawn.

Your opponent can make blunder's too and if you can apply a little pressure he may blunder or get defensive and give you the initiative you need to equalize or win.

Black is up a piece for a pawn, not down the exchange for a pawn.

One of the moves you suggested still drops the rook on e8. The other is illegal.

Rf8 and get the Knight off the back rank and into the game.

No - I must take back what I say above. Rg1(+) with Be5 is definitely a crushing plan. 1...Bf7 is unplayable, as after 2. Bf5 it will be impossible to prevent this setup, with dire consequences. 

please leave me out this beeping

That's what I was thinking. As black, I kept looking at those pawns that, I swear, got taller as they were marching up the board. He had those two bishops, both active as hell and for good measure, my king was naked unto the world. So I blunder, I check the analysis and I'm ahead? You and Solskytz have both provided great comments here (thanks to all who have commented, by the way) and I've been looking at the position for a few days now (it's a fascinating position). I just think Black is in real, real trouble which, not coincidentally, is how I felt at the time--in real, real trouble. 

It looked like it was only a question of "how many moves" before black swept white off the board - until the advent of IM PFREN upon the scene...

I'm sure that the study of this kind of positions is extremely beneficial to any player (me included). It teaches a lot about dynamics vs. material, and about the importance of crucial lines (the g-file, the e5-h8 area).

@solskytz:

After 1...Bf7, 2. Bf5 probably isn't the best move, since it gives the knight a strong development move ...Ne7 with tempo. A simple 2. Bd3 maintains the pressure on h7, and if the knight on c8 moves, then there are some nasty checks after Rg1+ and Bd6+, winning a lot of material.

I am not sure if black has any realistic chance for a draw here. What I would be interested in is looking at the game leading to this situation; it looks like black created some terrible weaknesses on the king side at some point and white managed to sacrifice a knight for a winning attack.

There are faster tactics in the position, it seems. 

1...Bf7 2. Bd3 is probably good as well - but 

1...Bf7 2. Bf5 Ne7 is unimpressive in view of 3. Rg1+, after which white either drops the knight on h7 or gets checkmated.

First of all White has compensation here and the game is even! Black is not better. White has sufficient compensation for the piece. For the piece White has 1. two passed pawns 2. dangerous highly active bishops. 3. Space advantage

The next moves are 1...Rf8 2.Be5 Nf6 3. h7+ Kh8 4.f4 Ne7 5.Bb1 Nf5 6.BxN BxB 7.Rh6 Bxh7 8.BxN Kg8 8.a4 and White is a bit better.

1...Bf7?? loses to 2.Bb1 Re6 3.Bf5 followed by Rg1+

I didn't mean playing ...Ne7 immediately, of course, but it could be a possibility in the future. I think backing up is more solid, and I'm not sure if on f5 the bishop is doing anything useful: attacking the c8 knight doesn't seem helpful, since the black rook isn't going away from the 8th line.

This is what the engine recommends, but in practice some moves other than 2... Re6 force white to play quite a bit more carefully. 1...Bf7 2.Bb1 Nf8 3. Rg1+ Kh8 4. Be5+ Rxe5 5. dxe5 Ne6, and, while the game is won by white, black can still struggle for a while.