You need to get the paperwork for your title. In some states this is automatic; you’ll simply get your title in the mail and have to retitle it without the lienholder. In other states, you might have the title in hand. In this case, you will have to get a lien release and go to the DMV to retitle the car.
While it might not be something you think about, you should also check your credit score. You may think that paying off your loan would result in a positive impact, most credit scores drop a bit due to a lack of credit from paying off your loan. You want to make sure that your credit report is accurate and reflects the car loan payoff.