how do you trade in a car that isn't paid off yet?

Depends on how much equity you have, if it's worth what's owed, and if the registration says "AND or "OR" you and the ex. If it says OR, you are ok. If it says "AND" they won't touch the deal without her signature

The dealer will add the balance you owe and add it to the new car purchase. BUT- check with your local Better Business Bureau first to see if any of the dealers you're considering have a record of not paying these balances in a timely manner. It's one of the largest complaints filed with the BBB against auto dealers.