How should I analyse my game to get better? I've been playing chess for a while, but very casually.  I just joined a chess club and played my first tournament game.  Not having used a chess clock before, or ever having had to record my moves made things interesting!

I really want to get better and I've heard I should be analyzing my games.  Other than stepping through them and figuring out if I should have done something differently (given I lost, probably), is there something specific I should be doing?

This is my game from tonight, any ideas/analysis would be very welcome.

[fen ""]
1. e4 c5
2. d3 Nc6
3. Nf3 e5
4. Nbd2 Nf6
5. c4 Be7
6. Nb3 O-O
7. Be3 d6
8. h4 h6
9. Qd2 Ng4
10. O-O-O Nxe3
11. fxe3 a6
12. d4 exd4
13. exd4 cxd4
14. Nfxd4 Ne5
15. Qf4 Qc7
16. Nd2 b5
17. b3 bxc4
18. Bxc4 Nd3+
19. Kb1 Nxf4
20. g3 Ne6
21. Nd2f3 Rb8
22. Rc1 Qa7
23. Nc6 Qe3
24. Nxe7+ Kh8
25. Rhf1 Qxe4+ {I realized this was a mistake as soon as I made it}
26. Rc2 Nd4
27. Ne1 Nxc2
28. Nxc2 Qxc4
29. Ng6+ fxg6
30. Rxf8+ Kh7
31. Kc1 Qd3
32. Rd8 Bf5
33. Ne1 Qb1+
34. Kd2 Rxd8 {i resign}
Opening

I feel that you are getting lost in the English Botvinnik system, seeing as you form the Botvinnik pawn triangle (c4-d3-e4) but then your piece placement is off (e.g. O-O-O instead of O-O). I suggest you visit my answer to Suggest a line for a player who does not want to be dragged into the Sicilian for more information.

Also, try not to move the same piece multiple times in the opening, as 6. Nb3 isn't constructive. I would try 6. Be2 and 7. O-O with a safe but cramped game.

Material

You concede the bishop pair (half a pawn) with 9. Qd2 instead of 9. Qc2.

The move 15. Qf4 is the start of your tactical woes. This square should set off alarm bells because of both the potential for a knight fork and pin (...Bg5 may become playable). I would have looked at 15. Kb1.

Tournament etiquette

Comfortably using notation and the clock comes with practice, but I don't understand why you carried on playing after 18...Nd3+.