I used to sell cars. Some of the advice in this thread makes sense, some of it is terrible. (Bring your girlfriened along and have her act like a bitch? Ridiculous.)

Go to the dealer to buy the car two days before the end of the month. They'll be eager to sell another unit that they can report as a sale for that month, and more likely to cut the price to make the deal.

If you finance at the dealer, be aware that there is profit in that part of the deal as well. You can often negotiate a better interest rate, and if you get a rate quoted from a bank or a credit union, the dealer may be willing to match it. They make more money by selling you financing as well as a car.

Find out if there is any money from the factory on the car. Just because the invoice price is X doesn't mean that the dealer can't go below X, especially on a badly-selling model. I don't know how well the Mazda3 is doing, but Ford, Mazda's parent company, often offers cash back and rebates and so on. Edmunds.com has that information listed somewhere.

If you want to be taken seriously by the salesman, conduct yourself professionally. Don't whine or cry or bed or plead. Remain calm and in control. If he asks for any information that you're not ready to give, you can reasonably say "lets talk about that later" or "I'd rather not say." Don't be shady -- if you've declared bankruptcy and you lie about it, they will definitely find out and you will not get what you want out of the deal.

Salesmen do not like to played off of one another. Calling two or more dealerships and asking them to "bid" on your deal is really annoying to a salesman. If you want to get quotes from multiple dealers, do so discreetly.