Get your car in tiptop shape. Trade-in values are based on the specs of the car itself, as well as the age, mileage and condition. While you can't change the details of the car, you can make sure it is in the best condition possible for very little cost. As you get ready to trade in your used car, get it thoroughly cleaned and detailed, though you may want to skip obvious signs of fresh detailing, such as tire dressing. You can do this yourself or pay someone $100 or less to do it for you.
If your car has any dents or dings, you may want to consider having those removed if that can be done inexpensively. Keep in mind the difference in trade-in values between the current condition of your car (such as "good") and the next level (such as "excellent") to get an idea of how much more you should be able to get for your car.
Negotiate the used-car trade-in value separately. When you are ready to negotiate your trade, do so only after you've negotiated the price of the new car you're purchasing. If the dealer asks you about trading in your car earlier, tell him you plan to keep the car or that you're selling it privately. Dealers can make it look like you're getting a great trade-in price by charging you more for the new car, so negotiate each price separately. Once you've settled on a new car price, ask for a quote for trading in your car. Be sure to get the trade-in value in writing.
Take time to think it over. Once you have the trade-in quote from the car dealer, see how it compares to the trade-in values you found in your research. If the trade-in values online are higher, show the dealer the printout from the applicable website and ask him to match the amount. If he says "no," don't hesitate to walk away, politely stating you were planning on more and that you need to think it over for a day.
You may get a better offer on the spot, but if you don't, don't worry. It's quite likely you'll get a phone call with a higher offer, especially if the difference between your two numbers isn't too much. In the meantime, don't hesitate to visit another dealer (or two) to see if you can get a better deal. Despite the urgency a dealer might convey, it's highly unlikely you'll be unable to get the same offer from a dealer at a later date.