What is the longest loan term for a pre owned vehicle?
Your dealership can arrange the loan, you may go through your own bank, or you may use a loan broker like Lendingtree.com (highly recommend).
On a 99-04 car, you might be able to go 60 months. Some banks may cap the loan at 48 months though.
Try lendingtree and see what terms you can get. I have used them beofre, as have some of my friends with good results.
If you get a loan from an outside source, All you have to do is let the dealer know who the source is. They will arrange all the paperwork with your lender (bill of sale, title transfer, etc). The dealer would prefer to arrange your financing as that is another profit center for them. Also, people with pre-approved financing are less likely to buy add-ons like warranty, VIN etch, Lojack, etc.
The dealer will offer to meet or beat whatever financing terms you have arranged. If they can, let them. You get the same deal, they get to make a little profit, and everyone wins. If they cant, you already have the best financing in your pocket.