1. Don't negotiate. Tell the salesperson and sales manager that you'll sign the paperwork the minute they hit your target figure. Politely decline any counter-offers, give them your phone number, and leave. If the price you've proposed is within the realm of possibility, they'll call you at some point.
2. Follow-up on Saturday or Sunday nights an hour before closing time. Call and ask to speak with the salesperson or manager you've spoken to before. Remind them you're a buyer when they meet your figure, but that they shouldn't waste your time if they won't.
If your offer is possible, the opportunity to do one more deal before the end of the day might compel them to work with you... especially if the dealership is having a bad weekend.
3. Follow-up on the last day of the month. Again, salespeople and managers are often under pressure to find one more deal before the month ends. A deal that didn't make sense on the 25th might make sense on the 31st if the month hasn't met expectations.
4. Follow-up on days that have had terrible weather. A major snowstorm, a day of wind and rain, etc. can dramatically affect car sales. Call and remind the salesperson or manager that you're happy to come down when they meet your offer. Again, the fact that they're not selling cars might get them to bend in your favor.
5. Rinse, wash, and repeat. Do the same process concurrently with a couple of other dealers in your area. Make sure they have the car you want, and then give them their mission.
6. Know what a car is worth. If you're buying a new car, Edmunds.com and TrueCar.com provide "true market" estimates that are reasonably accurate. If you're buying a used car, KBB.com is a great resource, as it will tell you both retail value and wholesale (aka trade-in) value.
7. Secure your own financing if you can. A great way to avoid the drama in the finance office is to get a loan from your local credit union. However, if you're buying a new car and you want to take advantage of a special interest rate (like 0%), you're going to have to work with the dealership's finance person.
Quite frankly, I don't see what the big deal is about going through finance. It's true that you're going to be brought into a small room with a very good salesperson, and that he or she is going to pitch you all sorts of stuff. You're an adult. You can handle this. Be polite, but say no to everything. It's not personal, it's just business.
8. Always be polite. In some of the other answers to this question, I've read suggestions about telling the dealer to "take it or leave it," threatening to walk out, etc. This is all bad advice.
There are a lot of things that suck about working at a car dealership, not the least of which is being treated like crap by most of the people you deal with. While dealership employees learn how to "warm customers up" - it usually only takes a minute or two to get a stranger to laugh and relax a little - it's emotionally draining.
In closing, the downside to my process is that you might have to buy a car late on a weekend, might have to buy a car during a blizzard, etc., but you'll get the price you want (or at least get closer than you ever thought possible).
Good luck!