Know your state's auto insurance requirements:
Most states require you to carry a minimum amount of liability coverage. Many states have "no-fault" auto insurance systems. Coverage for medical costs for you and your passengers is optional in some states. Coverage for damage to your car is optional.
Read your policy:
Yes, even the fine print! Ask questions. Keep your policy at hand. Call your insurer to keep your policy up-to-date, inform your agent of any changes (new car, new job, new driver, etc.), and ask periodically about any possible discounts. Review your policy yearly with your insurer.
Keep your auto insurance information with you:
Many states require drivers to carry a proof-of-insurance card with them when driving. Ask your insurer for a card, and keep it in your wallet or in your car.