A few comments on this game.
It's generally a bad idea to bring out your queen too early as your opponent can chase it around whilst developing pieces. You got away with it in this game because your opponent allowed you to exchange queens early on. In the opening you should be trying to develop your knights and bishop and castle before you start thinking about where your rooks and queen belong. You have to balance this with keeping control of the centre with your pawns.
Your wing pawn moves - a2-a4, a4-a5 and h2-h4 didn't really seem to have a point to them. Often these are better placed on a3 and h3 to prevent your opponents knights and bishops getting to a powerful square.
Your first real blunder was 23. Rd3. This is called an overworked piece. The rook is doing two jobs, defending the knight on c3 and the other knight on d4. Whenever you have an overworked piece your opponent is likely to have tactics which win material. This is exactly what happened here.
When you are material down, it is generally a good idea to try and keep as many pieces on the board as possible, but to swap pawns whenever you can. This is because you may get to a drawn ending (e.g. king and two knights vs king). If your opponent has any pawns left in the ending, he may well be able to promote it to a queen.