I bought a new Toyota Tacoma yesterday
I am probably repeating things that have been said many times before, but...
My advice (which I did NOT do) is: be willing to get up and leave the dealership. I really think this is your strongest negotiating tactic.
I am certain I could have gotten a better deal if I had stood firm on my demands - AND - if I had been ready to walk out. As it was, I really wanted a particular vehicle, and made the choice to take one of their offers.
Just FYI: there was an $8000 difference between their first offer and the one I finally accepted (on a $43K truck.) I think I could have saved another grand or two if I had been more resolute. If I had left and come back the next day and gotten another thousand dollars off - well, that would have been a pretty good day's pay. But, I got impatient.
I would also like to say, be kind to yourself if you don't get the absolute best deal possible. It is a tiring process, and not everyone has the luxury of spending an entire day (or several days) to shop different dealers. Sometimes good enough has to be, well, good enough.
Edited to clarify...
Their first offer included:
--- $0 discount off truck price
--- $12000 for my trade
The offer I accepted:
--- $2000 discount
--- $18000 for my trade