for the capitalone pre-approved loan it works like this
1) you apply for the loan for a certain amount (which is for more money that you actually need), for example $25,000
2) once you get approved you will get a check in the mail that you can use at the dealer
3) you negotiate for the price of the car, and you write that amount on the check, say $21,000.
whatever you right on the check becomes your loan amount, and you pay it off based on the interest rate and loan length that you were pre-approved for.
Once you have negotiated the price, you might want to ask the dealer what kind of financing deals they have. When I bought my car I had a capitalone preapproved loan, but I ended up not using it, because the dealer was able to beat the interest rate by 1%, with the same terms