Once you know, as well as you can, your and your opponent's BATNA, it's time to set the stage for the negotiations. These are the subtle things that provide one side an advantage before the first words are even spoken. The key components are timing, location, and environment.
Timing can be any number of factors. No car buying advice is complete without telling the buyer to come in at the end of the month. If you come into a store close to closing time, the salesperson may sweeten the deal to get you to buy quickly. I've been in many negotiations with people from outside the United States, and have repeatedly seen delay used to take advantage of the American's impatience. This works more often than I'd like to admit.
Location will usually boil down to home team advantage, but not always. While the person negotiating from their own office is more comfortable and will have most of their resources at hand, the visitor can learn more about their host by seeing them in their natural habitat. Of course, the host generally doesn't have to worry about catching a flight.
The Environment is the additional factors beyond location that can affect the outcome. Having your team in the room with you is an advantage, especially if you make up the majority. If one of you is standing out in the cold, while the other is in a warm car, the frozen party is more likely to make concessions to get someplace warm.
Of course it's possible to put too much emphasis on these factors at the expense of due diligence, but if the options present themselves, you can put yourself in a better position to succeed.