I somehow managed to win this game, and want further insight into how.  Please help!

I'm not sure, it seemed like the king had two other moves left...Maybe the opponent resigned?

...Yes, the opponent resigned.  That's not what I meant.

oh...what exactly did you mean then?

Was I unclear?  Sorry!

I want help analyzing the game.

Well first you sacrificed your pawns to bring out your knights, then you brought out your black square bishop, then you and the enemy began preparing for the clash where the white's furthest pawn was, then once the king castled you and him began swapping pieces there, then you went to attack his queen, and I guess he decided to give it up for your rook or just messed up thinking of a different idea and forgetting about your rook...Pretty much it seemed to me that the enemy kept piece swapping when he/she was at a disadvantage for it, so you managed to take out his/her pieces, then you were able to corner the king since it was trapped by its castling move earlier.

All in all, you played the better game.

Your opponent repeatedly blundered (no, there wasn't any point to him losing his queen) and didn't take advantage of your mistakes. Becasue of this, it seems to me that you think some of your weak moves were very strong. For example, 19...Ng4+?? What were you intending to play after 20. hxg4?

I see many bluders made by your  oponent. I suggest that  your rather analize games where you are loosing. I tend to learn more from my loosing games than from the winning games. Best of luck .