how do i finance a car through this site?

That would be between you and the private owner, but my guess is almost ALL private owners will not finance for obvious reasons. Since CarGurus is just an advertising site the financing will be up to you. My suggestion is to contact your bank or credit union.

You can't.

Yes, car gurus offer and AutoB Buy option where they can get you financing to purchase prom a private party

You would have to contact AutoPay to work that out.