Start by asking your current lender for the exact payoff amount, which includes accrued interest and often runs a bit above the statement balance. Check your own credit next so you know the tier you are shopping in. Then collect quotes from at least three lenders inside a two-week window, so the inquiries score as one. Credit unions are the natural first stop, since they routinely price below banks and dealer offers, and any federally insured one can be verified through
NCUA. Compare offers on APR rather than the advertised rate, because APR carries the fees.
After you sign, the new lender pays off the old loan and takes over the lien. Keep making payments on the old account until you have written confirmation it is closed. A payment missed during the handoff lands on your credit report like any other missed payment, and it is the most common way a clean refinance turns messy. Cancel the old autopay the same day you get that confirmation.