Getting the best price for a car is not easy... it can be pretty hard work. Stressful at best. The car dealers do it every day and are masters at it. They have very subtle ways of putting pressure on you.
Their favorite trick is called "hide the trade". Never, ever give them the keys to your trade in. If you do, it will disappear so they can "appraise" it. It will be hard to get back. So, if they want to appraise it... go with them and KEEP YOUR KEYS. It makes it hard to walk out if you can't find your car.
My best deals on new cars have been made over the phone before I even went into the dealer. Obviously, you need to know exactly what car and options you want to make this work.
It also helps to know what other folks are paying for the same car... so the internet (mostly forums) are your friend.
And sometimes... time is your best negotiator. The last used car I bought took no negotiating at all. It was a turkey... sitting in the back of their lot, languishing for months. Every couple of weeks they would drop the price on their web page... and when they hit my price (basically wholesale) I bought it. This obviously doesn't work with cars that are in demand.
Car dealers are so "old school". They have been selling cars the same way for decades. There has to be a better way... but, until there is, NEGOTIATE.