I am rated higher than you, but aside from the two blunders you mention, your play seems pretty solid. You calculated the value of the exchanges that you made and came out ahead, and the final move, f6, is pretty decisive. Nice play. Now, someone rated higher than I will no doubt chime in with lots of positional advice that neither of us understands, but I believe you did well. And your knights were very effective.
Beginner to chess, need tips or guidance on how I could have mated opponent?
Mating with a bunch of knights and bishops takes a lot of thought and isnt always possible. In complex and messy positions like this, its usually easiest to push a pawn and either get a queen or force him to trade a piece for it and repeat the process with another pawn. If you know how to mate with queen and king v. king, with king and rook v king, and with two rooks vs. king, thats more than enough at your current rating.

It's a nice game and you played really well as MSteen points out.
I will point out a few minor things I noticed.
Playing d6 and d5 on your 4th and 5th moves was not great. Loss of tempo.
I am not convinced by 6. ... dxe4. White moved the knight but he could have played Bxc6+ first in which case you would have to retake the bishop with your b pawn - leaving you with a messed up pawn structure on the queenside with lots of weaknesses you could pay for later in the game.
When you played 9. ... Bg4 didn't you just miss the chance to take a piece for free with 9. ... Nxe4? If so, that we a blunder by white (to leave a piece hanging) and then a blunder by black (to miss it).
White blunders again with 13. c3 by leaving the bishop on by hanging. Black can take it with the knight but also blunders by missing this and playing Nc2. In fact, Nc2 is a double blunder because not only does black miss that the bishop can be freely taken but Nc2 is a suicide move by the knight. It looks impressive, attacking the rook, but when the rook moves to c1 attacking the knight, the knight has nowhere to go. Black should be a piece down. Obviously 14. Bxc7 is dreadful by white.
18. Bd3 is another blunder by white. Well spotted by you.
I don't think you missed an easy mate at the end. But you played really well - two pieces and three pawns up - with a very easy endgame win.

Wow, thanks everyone! Msteen, I appreciate all of the positive feedback! Also, I will practice mating on my own in those situations you listed ArtNJ. And yes it seems pretty complex to mate in that situation I guess. And corum I am going to go through that analysis now and compare it to mine. I do agree there was a lot of little mistakes and times when I'm overall just not sure where to move yet. Missing the 9. ...Nxe4 was definitely a careless blunder.
Thank you all for taking time to help me, I appreciate it!
I think it might be hard to teach yourself the mating methods. I'm sure its in words somewhere, maybe wikipedia. No substitute for having someone gently smack your hand and remind you of the method when you do it wrong, but better than nothing.
A lot of very early stage beginners just take all the other person's pieces, get an extra queen and try to figure it out. Which can work, but is a good way to accidentally stalemate your opponent. Learning the checkmate methods with the combos I mentioned is definitely smart to do at your level, but I guess in the big picture, its probably no more (and maybe less) important than practicing tactics at your level. For that, I recommend a free account at chesstempo.com.
Wikipedia has an article called "Checkmate pattern" that is worth looking at.
"Chess 5334 Problems" by Laszlo Polgar is also good (for checkmates).
It starts with about 300 Mate in 1's; then moves onto several thousand Mate in 2's.

I am pretty sure you can find here on the website problems on how to checkmate if you go for a premium membership - no idea what level you need exactly although.
About the game, my biggest sugestion is - look at piece and count how many times both players are attacking and defending it - also inbetween moves with check!

@Pixenix Actually the beginner computer workouts are free. It's directly under Chess Mentor when you scroll over the Learn tab. I believe they do teach the endgames on chess mentor. You can then practice them with the computer workouts.

I think it might be hard to teach yourself the mating methods. I'm sure its in words somewhere, maybe wikipedia. No substitute for having someone gently smack your hand and remind you of the method when you do it wrong, but better than nothing.
A lot of very early stage beginners just take all the other person's pieces, get an extra queen and try to figure it out. Which can work, but is a good way to accidentally stalemate your opponent. Learning the checkmate methods with the combos I mentioned is definitely smart to do at your level, but I guess in the big picture, its probably no more (and maybe less) important than practicing tactics at your level. For that, I recommend a free account at chesstempo.com.
Just signed up for chesstempo.com...it's amazing! Thank you for this!
And yes I'm checking out the wiki now and all the sources on this website...Thanks a ton everyone!

Right now I'm analyzing 20... Nd4 which is either beautiful or just hangs a rook. I think the second, because although it's an idea, after 21. Rxd1 Ne2+ 22. Kf1 there is no compensation, and the whole thing is reduced to an "Ugly" trap.

I think you are very wise to ask yourself and the forum this important question at this early stage in your chess career. I have played many timed games on this site in which my opponent has gained and sustained an advantage during the opening and middle game, but then has been unable to finish the job so that I have ended up with a "lucky" draw or even a win. I think the simple principle that such players miss is to restrict the movement of the king. In your game, white's position is hopeless and your opponent probably resigned because of the fork g5+, losing his knight - but to illustrate my point Be4 would restrict the king's movement and give white less escape options. However, you should just keep this in mind as a general mating principle and follow the correct advice of the other posters of just promoting a pawn in most cases rather than worrying about achieving a difficult mate with the minor pieces.

I'm not sure about 7. Nh4. 7. Bxc6+ bxc6 8. Nd2 damages Black's pawn structure and avoids moving a knight to the rim.

- Look for development. The faster your development is and the more pieces you got controlling the centre the better. In the game you played d6 and the next move d5. Either choose d6 or d5 but the extra tempo you give away isn't good.
- Always look for captures and checks before you make a move. This will lead to many free unexpected material for you to take.
- Before you make your own move always look if it can be captured without compensation (compensation is: better stronger position, more development as a result, harrassing the queen etcetera)

7... Bg7? is not great either. (8. d5 where to stop the loss of your pinned knight your must give your Nf6 up for 2 pawns by 8... Nxd5 9. Qxd5 Qxd5 10. Nxd5 Bxb2 11. Rb1 e6.)
Hi all! I've been playing chess for a few weeks now when I joined this website...love the community! I have posted similarly before about getting some help, but this time I need help looking at my most recent game as black (in particular the endgame).
Also if there are any other types of critiques you can give for a beginner, I'd love to hear! I have really been studying openings and some tactics. This mate situation just stumped me! He happened to resign though anyways.
After analyzing the game on my own I realize I made some major mistakes early on such as the 9...Bg4 and 13...Nc2
So if you could help me determine the way I should have positioned my knights and bishop for the fastest mate, or give some overall chess advice, I'd be appreciative! Thanks!