Edited to say that note for 30 meant I though he would move Bb4 to e7 and follow up by taking my pawn

 

ummm... you guys both hung pieces :) and lots of them. until you get past giving up material blindly it is hard to make helpful comments about your strategy.

I agree, hanging pieces are my downfall too. I look for my move...then look for a better one.

To improve in chess the very first thing a player must do is to stop making obvious blunders, like hanging pieces or overlooking mate in one or 2. Until you have done this theres not much point in studying endgames or memorizing openings 20 moves deep.

can someone please point out the stupidest mistakes that were made or forced checkmates that were missed?

 It's my first online game against another person, so not much is all that obvious to me

5.....Nb4 is the first mistake that loses a piece to 6Qa4+ , which your opponent didnt see...6....Nxe4 gives a piece for nothing but a pawn ...after this black is simply lost objectively speaking

I was playing as white, and came off a lot worse than black by the end of the game

10...Nc2  White's bishop was hanging on h4 forv several moves. 27.axb4

 On 30...check escape takes priority 35.Bxa2 was good.

White was very lucky to get a draw.

Everything looks a lot worse after the game

Some of White's simple mistakes:

After 7. ... Bf5 your knight on e4 is attacked. Your opponent will take it with his bishop. You must either move the knight, or defend it so that you can take the bishop back in return. (You could also play Qa4+ and take the knight on b4. This may be best as the queen will then attack the b7 pawn, but this idea requires looking several moves deep, try to accurately look one move deep first!)

 

14. Nd2. Your bishop on h4 is attacked by a pawn. Black will take this bishop unless you move it. It is ok to allow black to take the knight on f3 because you will recapture his bishop. It is not ok to let your opponent take a bishop with a pawn when you get nothing in return. 14. Nd2 attacking the bishop is an attempt at a clever stall, but as you see, Black is able to play Bxg2 winning a pawn and attacking your rook. It seems white was unable to see black's best reply to 14. Nd2. You have to be able to look one move ahead!

 

"17. Ne4 Trying to get a pawn" You are still leaving your bishop in danger! 

 

19. h4. You allow your opponent to take your knight on e4. Again, failure to see one move ahead. 

 

26. Bc4. This is a little deeper, but you can win material by 26. axb4 taking your opponent's bishop. If his rook then takes your bishop 26. ... Rxb5 you can play 27. Ra8+ and after his king moves take his rook on h8. 

 

27. hxg5. You give up another opportunity to take black's bishop on b4. You have to keep your eye out for all possible captures. 

 

32. Rc1? You missed the chance to play 32. g7+ attacking both the king and rook. This wins a rook and allows you to promote your pawn to a queen! 

 

33. Rc7. This may be a difficult one for you, but 33. Rc8+ and if 33. ... Kxc7 34. Rxh8. If black tries to defend the rook with 33. ... Kh7 34. Rxh8 Kxh8 It will be checkmate with 35. Bf6+ Kh7 36 Rh1#

 

"35. Rxg6 Probably should have taken that with my bishop" You probably should have played Bxa2.  You've got to look at all possible captures. This is a failure to see even half a move ahead!

 

First, practice seeing all the captures that can be made. Never leave your pieces where they can be captured for nothing in return. Never let your opponent leave a piece where it can be captured for free, you must punish him for this. 

Thank you for pointing those out. I kept trying to look too many moves ahead and ended up missing simple combinations; I can't believe I missed 35.Bxa2! I think I was trying to keep from getting checkmated instead of looking for anything reasonable.