If this is your first vehicle then you need to indeed get insurance before taking over the ownership of a used vehicle in most states. If you already have auto insurance and are replacing a vehicle on your current policy the coverage might insure your "new" used vehicle for a few days. You will need to check with your state laws and insurance company though.
Before purchasing a new or used car, contact your insurance company to let them know about the car you might purchase. They should be able to give you a quote of what it will cost to add the vehicle to your policy, which can help you budget for your car purchase. Your insurance company can then let you know when you should call and add the vehicle so it will be covered.
Auto insurance comparision is a great way to get the best rate possible for your automobile insurance.