To maximize xp gain:

 - Buy XP boosts.  You can stack duration and per win boosts.
 - Play PvP instead of AI
 - If you insist on AI, play intermediate instead of beginner
 - Surrender if you can't win (to maximize games played)
 - Invite friends.  Referrals give bonus IP, which help you win (and get more exp)

<br />
However, I don't recommend trying to level up quickly.  IP is much more important for buying Tier 3 runes, and your time is better spent maximizing IP gain.


[Exp calculation][1]:
> Current (July 2011) formula for XP winning a Normal game at level
> 15-19 is roughly 3m+25, where m is the number of minutes the game
> lasts, capped at 198. Intermediate Bot games at level 10-14 use the
> same formula. At level 15-19, Intermediate Bot games subtract a 25%
> penalty from that formula, and give XP for only the first 180 minutes
> a day of play.
> Blockquote


[1]:http://leagueoflegends.wikia.com/wiki/Experience_(summoner)