There is still haggling at various dealers, especially the smaller ones. Places like Carmax have set prices, but their prices seem a little high.
Watch YouTube reviews of your model, go to Edmunds.com, autotrader.com, dealer websites, and KBB.com. That will educate you on the options available, and the pricing.
When shopping don’t give SSN or any personal information other than name, email, and phone number. Say you’re just shopping. Remember you are in control, without you there is no sale. If they try to pressure you move on.
Don’t get car fever, don’t say how much you love a car. Only talk to the dealers about what you don’t like. “Yeah this is nice but it’s got some scratches around the door handle”, “the floor mats are dirty”, etc. If you are prone to rash buying decisions, vow that you are not buying anything, just looking. You will probably want to go on multiple trips to see what’s out there with what options, you can check online first to see generally what’s available but nothing beats seeing it in person.
If you go to a traditional haggling dealer I always find it handy to negotiate on “out the door” price. Find a car you like, test drive it/get it checked by a mechanic/whatever, then offer $xxxxx “out the door.” That means that is the final price you will pay including dealer fees, tax, title, tags, etc. Otherwise when you agree on say $15,000 for a car by the time the financial guy finishes with you you’ll easily owe $16,500. Make a reasonable offer, but on the low side. If you think you can get the car for $15,000, offer $14,000 or even $13,500 and see how it goes. You won’t insult them and they won’t accept any offer that doesn’t make them money.
When you make your offer the salesman might act all flustered and say he doesn’t think his manager will accept that, but he will go off and make a show of talking to his manager, and then will come back either saying they can do it or with a counter-offer. Usually you will get a counter-offer. If you made your offer low enough, hopefully you can meet in the middle somewhere and be happy, or maybe you can ask more for your trade-in or get them to make some sort of concessions to support their higher offer. Otherwise don’t be afraid to say “No thank you” and walk. They can contact you if they want to make another offer or accept yours, and they often will.