The main thing you will need to show the insurance company is a copy of your vehicle registration issued in the current state and your driver's license. If you can bring in a copy of your old policy or insurance card, the new company can tailor a new policy that closely matches the old one, but you do not have to bring that information to apply for new coverage.
The vehicle registration is important for the insurance company because it tells them everything they need to know about the vehicle that will be insured. Even if you do not have a current registration, copy the VIN located in the corner of your driver-side dash board, next to the windshield. This sequence of letters and numbers identifies the car completely, including whether it has airbags and other safety features, how many doors, and the type of engine.
Your driver license is important to allow the insurance company to review your driving history. If you are applying online, enter the VIN number and DL numbers and the system can access the rest of the information automatically. These two pieces of information are necessary to provide you an accurate insurance quote whether you do it in person or by logging into a website.
If there are after-market items that have been added to the car, you may need to show receipts to the insurance company in order to get them properly insured. This could be a more powerful stereo system, gold-plated rims, or any other improvement made to the vehicle after it was manufactured.