I've done this twice. Once, they used an in-house financing company. I did this to get more money knocked off the price of the car. They run your credit, take out a line of credit, and you sign on the dotted line.
The last car I used this method in the dealership was 2004 and they gave me an option of using a local credit union because the rate was lower. That was just as easy...
One thing you can always do if you don't like the rate you get is go rate shopping after you secure the loan and get a payoff quote. Car loans don't have closing costs so you only come out on top if you refinance...unless it dings your credit score by adding too many new lines of credit to your account. (I didn't do this stuff often so it didn't matter much to me)
I misunderstood the question....I answered as though I used the financing options through the dealer. If you secure financing first, you need to contact the lender and basically do the preapproval thing.
These days, most will ask you for a VIN number before they proceed. You'll have to get an official document from the dealership with the vehicle information that shows the purchase price, VIN, your name, etc...I forgot what they call it....but it's basically what the underwriters base rates and collateral on. After the lender gets this, they'll cut you a check and start charging you interest on the loan. I went through this process back in December. It wasn't too bad, but the dealership was 200+ miles away, so it took faxing/mailing to get everything lined up prior to me driving to pickup the vehicle.
My cousin did something similar, but was somehow able to get a check written for $30k. He used that as a negotiation tactic in the dealership. He said, can you take $30k for this $33k car? When they started to say no, he said tell your manager I have this check...I can sign it over to you right now. It put the ball in his court. My credit union wouldn't give me a check without the car buyer's agreement in their hand.