Black to move and win in great style.

well, my rating has tanked over 200 points in the last two weeks so I should know a good blunder when I see one.
Rd2 looks good

7679369

First thought is Rd2, attacking the queen. White can't take with the Knight because it's preventing mate, and the queen is more or less trapped. White can throw the check with the pawn, of course, but doesn't appear to gain much other than a little time and the Knight on f6.

7679381
7679397
Indeed. Even after exf6 and exf6 the queen can't leave due to Qxg2#. White went Ngh4 instead and decided to play with a rook and knight for a queen, so I played Rxe2 and he replied with Rxe2. I played Rd3 and he played Rfe1.
Apparently at this point I should've played b5, but I didn't even look at the queenside and played g5 instead. fxg5, fxg5 and apparently the only way for white to survive is Kh1 (if gxh4, Ng5! and black has to give back the knight with Nf2+ to avoid losing the queen).
However, my opponent played Nxg5? which brings us to the final blow:

I guess you'll find this move without any problems.

I'm behind on messages, but I don't see an answer for d3.

7679763

I may be way off, but a continuation could be Rxg3+, hxg3, Qxg3+, Rg2, Qxh4, forking the knight and rook.

7681933
You're right, up to some point. After Qxg3+, white has three options, all of them pretty bad:
1. Ng2 Qh2+ Kf1 Qh1# which happened in the game.
2. Rg2 Qxe1# since the rooks no longer defend each other.
3. Kf1 Qxh4 and the knight from g5 can't be saved either due to the threat of Qh1#. This line doesn't lead to forced checkmate, but two pawns and two minor pieces for a rook are enough to win.

7681808
Rd3? I think white then plays Ngh4, defending the knight with knight.

7681989

Indeed. Just curious, what are your thoughts on Qxg3+, hxg3? I'm having trouble seeing the options for black after that.

7682082
As in, giving up the queen? White is up two pieces after that.

7681989
Hmm. I was thinking that would follow with Rd2, but now I think Rd2 first is more effective because the knight square is another easy mate as long as it isn't defended.

7682200
Yeah, this is why rook and knight for a queen is the best white can hope for.