Most important.....Dont tell them you have a trade in. They'll just base the new cars price on your trade in and you'll realy end up just giving your car away. Don't fall for the "they gave me such a good deal on my trade" crap. What good is $10K trade for your beater honda/toyota/etc if they just raised the new car price $10K too.
And don't tell them what you want to pay "per month."
Salesmen see buyers as "trade-in people" or "monthly payment" people. So don't show them your cards.

AS others said...negotiate the "out the door" price only. New or used, they'll try to hit you for all kinds of bullshit after you settled on the price. Don't EVER pay DMU (dealer mark up) its bullshit. Its just extra money they make. Walk if they won't budge. They'll stop you before you hit the door. After you make a deal, then decide to trade-in your car. Come with all kinds of data; KBB, Edmunds, etc. Have in mind what your car is worth in this market. And that's trade-in value, not resale.

Rainy days are good time to buy, at the end of the year, and the end of the month, they are more willing to deal.

Also, see if your business works with buyer incentive programs. Often larger companies partner up with car makers to offer low prices to employees. Sometimes you can get a car at dealer cost (they still make money on something called Dealer Hold-backs)
Ford has something called the X-plan and Chrysler has something too. Ask around at work.
I paid $15,700 for a SVT Focus brand new in '02. Sticker was $22k. I had the x-plan price.

Always, always , be prepared to walk. Don't let then see you "fall in love" with the car.
There are plenty of others out there just like it, and dealers know it.