Okay, just a couple of things that other people have said or that I think are of note:
Make sure you have a _clear_ goal and grievance. By this, I mean don't go gunning for the AP's head just because she's objectionable. If you want to start a D&D club, then _that_ is your goal and don't go after her. If you think she, herself, is objectionable and should be remove, then that is your goal (but leave D&D out of it).
Whatever you're going for, it will be best served by keeping it pure and simple and unmuddied by a vandetta. I'd _strongly_ recommend writing down what you would consider terms of victory. Now, see if you can shorten what you've written. Here's a hint: drop anything that will naturally flow out of any other listed goal. See if you can get it down to one succinct sentance.
You might even tape it to the inside of your locker so that you don't lose sight of what you want to do.
Enlist aid. Get parents involved. Get teachers involved. Accept that those who offer aid are genuinely trying to help. Listen to them and take their counsil. You may have more passion in this matter, but they have more experience in dealing with things. Share your "victory conditions" with them. Let them know exactly what you are going for. Don't do anything without talking to someone else (it adds perspective).
You are going to get some of your best adult support by posting a sign in a gaming store requesting help.
Remember, you are not losing control by seeking counsil. You are gaining power, knowledge, and insight.
Avoid even the appearance of inpropriety. Don't _ever_ call the AP a name. _Ever_. Not even in private. Not even in your head (sometimes people forget what was said silently and what was said aloud). _Always_ treat her respectfully. _Never_ raise your voice to her. Do this even if you decide your goal is to get her fired.
If you need to object to something she does, object to the action or to her decision, not to her. Don't say that anything she does is "stupid".
If you are serious about this, I _strongly_ recommend you read "How to Win Friends and Influence People" by Dale Carnegie. I'm as much a fan of pointless arguing on the Internet as anyone (maybe moreso, even), but if you really want to accomplish something, this is _the_ book on how to conduct yourself.
Understand the scope of your opposition. You may be facing more than your AP. Know how big of a battle you're willing to fight.
Also, don't think you are fighting all Christians or all fundimentalist Christians. My gaming group consists of two Lutherans, a Presberterian, an Epicopalian, a Baptist, and a Catholic. All are very religious and most are active in their church.
What you're facing is someone who is being closed-minded and narrow. She may be on a power trip. She may simply be ignorant and trying her best. Who knows? Regardless, keep your comments in line with the scope of what you're dealing with. I know that as a strong Christian, I get as annoyed with people who bash Christianity as with people who bash gaming and that doesn't make me want to help them.
The same could be said for administrators. You aren't fighting everyone in power. Just this woman. If you insult "the school" or "adults" or whatnot, you are going to lose support. Do not alienate anyone.
Be informed. Follow some of the links the others have posted. Read the information there -- both pro and con. If you can, find information that directly refutes or post-dates (a study done later) the information that is opposed to your position. Another tack to take is to show why a piece of information doesn't apply ("Yes, I understand that says D&D is an unChristian activity, but since this is a state-run agency, you may not require me to be a Christian under the First Amendment anti-establishment clause." Citing a court case really helps.).
Put your arguments in writing. Don't go overboard (oxboxes are great for debate club, but bad for daily life), but have some basic arguments written up, supported by evidence, should you be asked to submit anything. This is even great for getting people's attention if they don't have time to talk to you immediately ("Well, then, please just read this and consider what I'm saying.").
If your school has a debate club, talk to the teacher associated with it. My experience has been that these are some of the most approachable and open-minded people. If you're not comfortable talking to the teacher, talk to some of the upper-classmen debaters. Trust me, they aren't that intimitating. Most of them would probably help you just on the hope that you'd get interested in debate. As an added bonus, it seems a disproportionate number of debaters have lawyers as parents.
Hope that helps you. I know my advice is a lot of work, but if you really want to go for this and do it right, that's what it's going to take. If you do this, it'll almost certainly be the most valuable skill you develope in the entirety of high school.
