First, the shameless plugs for two articles that I've written here. They may or may not be of help, but the comments certainly could be. Read 'em. See if anything fits your situation.
First, I've got a few questions: Do you live there year round? Do you have your own place? If you answer "no" to either of these, you may want to reconsider this whole idea. Someone who spends summers away from the area they claim to want to govern isn't a good candidate. Neither is someone who lives with their parents, OR drunken roommates.
Next, the sage advice, from another undergraduate student with big ideas about how everyone should live their lives ;-). You're gonna need exposure, and shitloads of it at that. Seems to me that you've got two options - solicit volunteers, or cough up some significant amounts of cash. You'll probably need both. Volunteers abound on college campuses - most people our age aren't even registered to vote, let alone politically interested. But the funny thing is, if they see something (read: can be made to see something) as "sticking it to The System", they're happy to take a half hour to march, chant slogans and staple up fliers. Virginia Tech has marches and fliers for everything from human rights, IMF/WB protesting and abolishment of Columbus Day to Goats' Rights (yes, I'm serious - it was one of the biggest and practical jokes I've ever seen. I'm guessing fraternity pledge prank...) Enlist some people to help you *politely* knock on doors, hand out literature at red lights and put up a web site. As for the cash - make some rich friends, and fast. Specifically, find some professionals who have voiced displeasure over something done by "the current system", and ask for their support. Also a good idea - dig through newspaper archives - find the letters to the editor. Anyone willing to pen an old-fashioned letter to complain about something would be a great advocate to have on your side. Find people who have the same views you do, call them, introduce yourself, your ideas, and ask if they'd be willing to support you.
You're also going to have to deal with the "age thing." Us damned kids get no respect. Distance yourself from being a "damned kid." Instead, you're an "entry-level professional" (hopefully you HAVE held a professional job, and can use that...) and an "aspiring professional" and a "future Austin business owner." Your best chance is to reach out to the young and/or disenfranchised, which shouldn't be that hard to do, given the current economy. They're looking for work and worried, you're looking for work and worried. Play that angle up, heavily. Your opponent (from now on, he has no name, and thusly no face or history to associate with it) is set for life, and has lost touch with the majority of his potential constituents. Repeat that until people start remembering it. Then repeat it some more.
Be careful not to slam your opponent. He'll be able to dismiss you out of hand as a "naive student," but you can't return "pompous old fart." Show vast respect for those with more age and experience, and emphasize how you realize you don't have the expertise to run a city single handedly - you'll HAVE to ask the people for their opinions and ideas. Emphasize how your opponent (the nameless, faceless man) won't ask for help, and people have no way of knowing whether their voices will continue to be heard. Experience can be a liability in politics. Use that.
Emphasize that you'll have more time to devote to the job than your opponent. You're single, young and energetic. You'll work tirelessly to serve the people.
Look up your opponent's past voting record. If he's held that seat for long, he'll have quite a nice list of things he's voted on. Look through it, find the inevitable screw-up or favor to a friend, and have someone ELSE leak it. You can't afford to be seen as a juvenile mud slinger, but you can't afford to not take advantage of mistakes your opponent has made in the past.
That's just off the top of my head. More later...