This strategy has worked well for me:
1) Do your research ahead of time. Pick out the exact options you require, color, etc. Always say that you are "just looking". Never fall in love with a specific car. Never go into a salesman's office. Never accept their business card. If they start bothering you, get in your car and leave. Research the dealer's cost. In the spring (March or April), Consumer Reports has an auto issue that is good for prices and repair records and features comparison.
2) Armed with your model and list of options, call the dealership and ask for the sales manager. (He doesn't have to pay a commission to any of his salesmen on this deal.) It is best to buy at the end of the quarter (end of September, but you may not have time to finish the research) or end of the month. I call about a week to 10 days before the end of the quarter or month.
3) Tell the sales manager that you know how the game is played. You have a list of options you want and you are buying a car from someone this week. No trade-in and you are paying cash (no loan needed). Don't be cocky, just confident and business-like.
4) He gets one chance to give his best offer. He'll suggest that you call the other places first and come back to him. No. He can choose to make an offer or not. You are calling other dealers. Mention that if the price is too high locally, you are willing to drive to Columbia or Omaha or St Louis to get the best deal from someone else. Ask if he wants your purchase to be included in his numbers or someone else (an out of town dealership). Most smart sales managers will make an offer.
5) Look at the offers compared to the Consumer Reports dealer costs. If they are too far off from cost (he can live with $500 profit or even less to make his numbers at the end of a month) then call in a wider circle (Columbia, Topeka, Omaha, Des Moines, St. Louis) until you have a reasonable price.
6) Be careful on the back end of the deal. AFTER you agree on price, they will try to sell you all kinds of crap you don't need. Undercoating, soundproofing, extended warranties, etc. You don't need ANY of that. It is just a way to get more money for almost nothing.
7) If you actually have a trade-in, then AFTER you have agreed on price for the new car, ask how much they could pay if you decided to trade-in. Don't be offended, it will be VERY low. You can sell it yourself for a better price. Use kbb.com to get the "private sale" value and put it on Craigs List.
Good luck!