An auto loan payment is driven by three inputs: the amount financed (vehicle price minus your down payment and any trade-in), the APR, and the term (the number of months).
The lender uses standard amortization to spread the loan into equal monthly payments. Early on, a larger share of each payment goes toward interest; over time, more goes toward principal. A longer term lowers the monthly payment but increases the total interest you pay over the life of the loan, while a larger down payment reduces both. The best ways to lower your payment are a bigger down payment, a lower APR (which is driven largely by your credit), or a shorter term if you can afford the higher monthly amount but want to pay less interest overall.