How does a car trade in work? Serious answers only!?

[lonely]

I currently have a car that I owe $14000 on. The trade in value is about $9500. I am wanting to get a different car and I don't know how that whole thing works. I know that I would have to pay the new loan and the old loan but would it be the old loan minus the trade in value? Meaning would I pay the new loan and $4500 or the whole $14000? I love my car but the loan is combined with my ex husband and I really want to get out of it with out ruining my credit. Thanks