Step one: price, only price
Negotiate the out-the-door price before mentioning trade, payment, or financing. Everything blurs once monthly payments enter the conversation — that is the point of mentioning them early. A written out-the-door number (with tax and fees) is the only comparable currency between dealers.
Step two: financing against a real benchmark
Walk in with a credit-union pre-approval and let the dealer try to beat it. Dealers mark up rates for profit — a legitimate 1–2 point spread exists. If they match, fine; if not, use yours. Either way the APR decision happens on numbers, not on the payment fit.
Step three: the decline list
Extended warranties you cannot price, tire-and-rim packages, paint sealant, VIN etching, "appearance protection." Some are occasionally worth it (an honest GAP policy on a small-down-payment loan genuinely is) — but every one is negotiable or declinable, and the finance office's margin lives in them.