How could I have won this?

This game puzzled me, and I figured it'd be worth analyzing for my benefit.  How could I have won this?   Where were my and my opponents' major blunders?

Also, If anyone could explain what the heck 1.h3 is good for, then I'm all ears!

1. h3 is utter crap. There is nothing to explain.

2. You need to protect your pieces better. In the middle game you ended up with one pawn down wich creates problems later in the endgame

3. You should not trade if you are a pawn down. It turned out ok because your opponent messed up and gave away his lead to a drawish rook pawn ending.

4. There is nothing you could have done in the end. Rook pawn like that draws if the enemy king gets near the corner. Still, you should maybe look up what opposition is. It helps in king and pawn endgames.

1.h3 ,I think, is just a wasted move.

h3=poop

17.e3 till the capture on move 20 are wasted at the very least,

hole at d5 pawn, your capture with your bishop and the use of threatenening that knight with be6 was bad

after white threatened your knight at bf4, you could have put his/her king in check and then move your knight

instead of moving your bishop at move 7. threatening whites knight with your pawn would have put on whites knight and create an even more imposing center

im no expert<-----900 rating in blitz games, just trying offer alternate moves rather than eye for an eye

in case i sound like a jacka** or trying to be something im not

have a good day

One thing I noticed about the character of this game.  The both of you were content to trade pieces.  That in itself will point a game toward a draw.

h3 couldve been a 'safe move' that they used so they could see what type of open youre going for. itsd not really strong in any regard, but for a defensive player (which really, this guy didnt seem to be) it could make sense.

at move 20 you should have played r-d3.  you "trade off pawns and it leaves his pawns fractured.  You actually end up winning the "new" e pawn after fxe and rxe.  then you can even put pressure on a new point with n-e5.  That seemed to be the  point that jumped out at me.    

Baffled? You played the opening beautifully up to move 6. His 1.h3, as everyone has mentioned, is pretty much the same as not moving at all, it throws away his first move -- in effect you are the one playing White... so you played in effect a Queen's Gambit... so we have a Queen's gambit with colors reversed. When he played 6.Nc3 you needed to see (calculate) that 6...Nf6 was going to lose a pawn (which is what happened). You had better: 6...d5 looks promising IMO.

Look at the position after 12.Qc2 ... what do you see? You have castled and developed your minor pieces; his Kingside is completely undeveloped and his King is in the middle. You needed to play aggressively and actively, mobilize your rooks and get some lasting advantage from this temporary one. If you play slack, he gets his pieces out and it's an even game.

12...Qf5?  horrible... all this does is give him a free tempo. He trades, you recapture, and now it's _his_ move. What have you gained? Nothing, you've just handed him a free move, and exchanged your actively posted Queen for his relatively passively posted one. 12. Rad8 fighting for control of the open file and keeping his king in the center is much better, I think. 

15.Rxd5 ... this is nonsense on his part, and his 16.f3? is bad althouh at least he's playing with an idea (shutting down your bishop's diagonal)  But you make nothing of it. You own the e-file. You have much more active pieces. You must analyze his position, find a weakiness, and attack it! Otherwise your advantage evaporates.

here's an idea... 16...Bb1!? Now if 17.Kxb2? Rd1+... winning back your piece and pinning his miserable N and R. Your one rook immobilizes both of his remaining pieces... neither can move without losing the other! Now you can manuever your N freely to continue attacking. 

Instead you play e4? You are helping to free him from his self made prison. 

For a player with a rating under 1500 you are doing a GREAT job of not hanging pieces, not making big material losing blunders. That's a first important step! But the next step is not making _simple_strategic_ blunders. I'm not talking deep strategy here, I'm talking abc's of strategy. Trading pieces only when it's to your advantage. Not helping him out of a cramped position with pointless 'attacks' and pointless pawn moves.... Your play on his kingside from move 15 on is a study in what not to do. I'm not trying to be mean, just help you improve. You trade and push pawns and just generally free up his position. Honestly he plays even worse than you. It's like he doesn't want to use his pieces, and you have to convince him to.  And you do :(

I strongly recommend you start studying Jeremy Silman's Reassess Your Chess, there's a lot there, you don't have to master it all in a day or a year, but dip in, study the stuff that interests you... I think it will help you play better chess.

*edit* An important note:  -- my idea: 16...Bb1!? Now if 17.Kxb2? Rd1+ ... that is great, but of course it's predicated on White playing a blunder. One must never make a move that depends on the opponent making a bad move. The real point of 16....Bb1!? is 17.a3 Ba2 with the idea of 18...Bb3 which gets control of the d1 square for your rook to penetrate his position.

It's nice to play a move which sets a trap for the obvious reply, but it must be sound against the best reply... I believe 16...Bb1 meets that criterion.

The first thing that jumped out at me was at move 25. See the diagram below and be sure to look at the Move List.

Yes. Ryannolt's suggestion works with the same weak e1 square and pin on the N and R that I suggested targetting a few moves earlier. It's like White just doesn't understand he needs to use his pieces! Ya gotta punish him for his sins! After 26.b4? you still had Rf1.

Remember this old saying: The pin, she win!"

Thanks so much for all your help!  I appreciate the ideas, suggestions to help further develop my skills, (especially JG27Pyth) and general demonstrations of "how to think".

Chess.com and many people on it are awesome!

Matalino, yes, that was exactly my point. Just click the Move List and you'll see a variation in blue. Those are the moves I suggested.

The end game is a simple win for White after Ke4 at move 40.

heck, If you feel like playing utter crap 1. a3 is better.

First, 4... Qb6 5. dxc5 Qxb2 favors black.  That c5 pawn is eventually going to fall, and then you will be a pawn up.  White gets a little bit of compensation, but not nearly enough.  Thankfully, 4... Nc3 5. dxc5? worked out fine (white should have played e3)

7... Be7?? was foolish, you completely neglected e5.  There are complex answers, but the simplest defense was Be6.

12... Qf5?? again, was foolish.  Moving the same piece twice isn't what concerns me (although it is a concern), but I literally fell out of my chair when you offered to trade off queens when down in material, and up in development.  It was the LEAST principled decision you could have done short of hanging material.

16... e4! was a dang good move

17... h5? left me on the floor again.  Ne5 was best (after Nd3-Bxd3-Rxd3 you are guaranteed a pawn back), but at least move your king closer to the center, don't give me heartattacks by randomly throwing pawn forwards without a reason (no, "space" is not a reason when 3 pieces a side are on the board)

19... Bg6? was a blunder for a very suttle reason.  f4! would have sucked the life out of your knight like a vampire, which could no longer reach d3

On move 21 you should have moved the knight to prevent BxN and a cripped pawn structure.

On move 25 Re1! won the exchange via a pin.

26... Nf3?? traded off your well developed and powerful knight for a knight on the first rank.

31... Re7 should have been played to prevent white from slipping to the seventh rank.  I don't see how black can force a win simply by pushing his f pawn, so I think this was nessecary.

32... f4 on the other hand was perfectly sound, as Rxb7?? would be suicidal.

37... f2+! 38. Kxf2 Rxc3 was an easy draw

41... Kd6?? was a game losing blunder after Kd4! gaining the opposition, read up on the opposition and king vs king and extra pawn endgames to find out why.

I've run out of time to analyze however >_>