Check your university brochure. If you come to the U.S. on a J-1 visa (given to exchange students) and want to drive a car, you need to bring an International Driving Permit. Your university will give you a comprehensive insurance policy to register and drive a car.
Rent a car if you'd like to drive once in a while. Renting a car is easy with an International Driving Permit. You can either get a non-owner's insurance policy from a local insurance agent or insurance available from the car rental itself.
Call for quotes and shop for the best rates on a non-owner's policy. You may not have an established driving history, so your premium is likely to be higher.
Get a guardian through your university's exchange student adoption program. Check the availability of a guardian with your exchange program coordinator. You can then add your name to their existing insurance policy temporarily and pay them for the difference in their premium.