First of all, paying cash does not help the dealer it just makes the deal easier for the manager. He doesn't have to worry if the deal will get financing approval.
Dealers and car companies make money on financing and often tie incentives to financing.
Now lets get down to the brass tacks of how to get the best deal. The most important thing is to know the dealers cost of the vehicle you want BEFORE you walk into the dealership.
There are a lot of web sites that will provide the cost (usually at a price), but the easiest way is to take the retail price on the sticker and multiply the price by 88.1%. That will usually get the cost within about $150.
Next when you go into the dealership you must be ruthless! Get the salesman out of the way as soon as you sit at the desk. He can't make any decision and will always have to "go check with his manager" to get anything done. That is a way to wear you down and make you give in to the price they want you to pay. Work only with a manager.
Once you get the manager, explain to him that you can buy today if he meets your price. If he agrees then low ball him. He will do the same to you so,, don't feel any guilt. Remember this is a game and the best player will win the day.
You should know about what the cost is by now, so offer at least $1000 less. Make him almost laugh at your guts.
Say "no" at least four times and then get up to leave. Don't worry, you can always go back to where you were and you haven't lost anything. Remember it is your money you are playing with, not his.
If the manager offers you a look at the invoice, make sure it is from the factory and not something that the back office typed up so he can show it to customers. You will know if the cost figures are in line with your information or not.
Also look for little things like the factory logo or the lack of any logos to give you a clue. A true "from the factory" invoice will always have the "Ford" or "Honda" or "Toyota" logo on the paper.
Once you get the price you want, then and only then tell the manager you are paying cash. He will depend on making and extra bump in finance so he will be willing to give a little more on the price.
Best of luck, and let me know how it goes. - Gary