* The lender (bank or credit union): You should contact them to get the title (proof of ownership). They'll likely mail it to you after the final payment is processed, but you may need to follow up if you haven't received it after a reasonable timeframe (a few weeks).
* The DMV (Department of Motor Vehicles): If you've moved since you bought the car, you may need to contact your local DMV to update your address on the registration. You may also need to contact them if your lender doesn't send you the title directly.
In short, you don't need to "get" the car, you just need to obtain the paperwork that proves you own it.