The most important negotiating advice in all circumstances (including this one) is to do some specific prep.
Firstly work on what negotiators call your "BATNA" (best alternative to a negotiated agreement). Figure out what it is and see what you can do to improve it. In this case, it's another dealership with a better offer or figuring out you can stick it out with your beat-up car a bit longer or whatever. But think through what happens if you can't agree. Then your decision is very simple. If what they offer you (when all's said and done) is not better than your BATNA you walk away. Don't allow yourself to be put under pressure to do a deal you don't like.
The second piece is to be super-clear specifically what your payoff is (in this case price) and maximise that. People often try to confuse the picture by getting you to negotiate on stuff that isn't to do with your payoff (eg throwing in a higher spec or free servicing or high-lifting doorhandles or whatever stuff you don't actually care about). Getting finance before you walk in to a dealership is part of this strategy - what you're doing is taking away levers that they could otherwise use to get you away from negotiating about your payoff or get you to compromise on your payoff itself. If you consider you have a finite number of negotiating bullets you want to spend those maximising your payoff and they are trying to get you to fire off-target.
Next-level thinking on the payoff question is to think about what their payoff might be and try to use that to your advantage. You can often "concede" things you don't actually care about that increase their payoff but don't really cost you anything in return for an improved payoff for yourself. You will absolutely miss this if you have a "zero-sum" mindset. Not super-applicable here but an extremely important and overlooked concept in negotiations in general. You can also use knowledge of their payoff to strengthen your hand. Like say you knew when the sales quotas for the dealership came due or that a new model of this particular car was about to come out - the sales person might be under extra pressure to sell which would improve your bargaining power.
Final point is check your ego at the door. You are trying to maximise payoff not "beat" the other side in the negotiations. Not everything is a zero sum game and if you get too concerned about an ego victory you are probably sacrificing some payoff you could otherwise have had. It's fine for the other side to think they absolutely took you to town if you get everything you want from the negotiation.
Firstly work on what negotiators call your "BATNA" (best alternative to a negotiated agreement). Figure out what it is and see what you can do to improve it. In this case, it's another dealership with a better offer or figuring out you can stick it out with your beat-up car a bit longer or whatever. But think through what happens if you can't agree. Then your decision is very simple. If what they offer you (when all's said and done) is not better than your BATNA you walk away. Don't allow yourself to be put under pressure to do a deal you don't like.
The second piece is to be super-clear specifically what your payoff is (in this case price) and maximise that. People often try to confuse the picture by getting you to negotiate on stuff that isn't to do with your payoff (eg throwing in a higher spec or free servicing or high-lifting doorhandles or whatever stuff you don't actually care about). Getting finance before you walk in to a dealership is part of this strategy - what you're doing is taking away levers that they could otherwise use to get you away from negotiating about your payoff or get you to compromise on your payoff itself. If you consider you have a finite number of negotiating bullets you want to spend those maximising your payoff and they are trying to get you to fire off-target.
Next-level thinking on the payoff question is to think about what their payoff might be and try to use that to your advantage. You can often "concede" things you don't actually care about that increase their payoff but don't really cost you anything in return for an improved payoff for yourself. You will absolutely miss this if you have a "zero-sum" mindset. Not super-applicable here but an extremely important and overlooked concept in negotiations in general. You can also use knowledge of their payoff to strengthen your hand. Like say you knew when the sales quotas for the dealership came due or that a new model of this particular car was about to come out - the sales person might be under extra pressure to sell which would improve your bargaining power.
Final point is check your ego at the door. You are trying to maximise payoff not "beat" the other side in the negotiations. Not everything is a zero sum game and if you get too concerned about an ego victory you are probably sacrificing some payoff you could otherwise have had. It's fine for the other side to think they absolutely took you to town if you get everything you want from the negotiation.