Almost every state requires car insurance before you drive. Without it you can lose your license and pay large fines, and you would pay for an accident yourself. Minimum amounts differ by state; see In your state.
The main parts of a policy
Liability: pays for injuries and damage you cause to other people and their cars. This is the part states require. It has limits written like 50/100/50: up to $50,000 per injured person, $100,000 per accident for injuries, and $50,000 for property damage.
Collision: pays to repair your car after a crash, whoever caused it.
Comprehensive: pays for damage to your car that is not a crash, such as theft, fire, flood, hail or hitting a deer.
Uninsured/underinsured motorist: protects you when the other driver has no insurance or too little.
Medical payments or PIP (Personal Injury Protection): pays medical bills for you and your passengers.
A deductible is what you pay yourself before insurance pays, for example the first $500 of a collision repair. A higher deductible makes the price (the premium) lower.
A car loan or lease usually requires collision and comprehensive.
About a dozen states use a no-fault system: after an accident, your own insurer pays your medical bills through PIP first, no matter who caused it. If you live in one, PIP is required.
Insurers look at your age, where you live (ZIP code), the car, how far you drive, your driving record, how long you have been licensed, and in many states your credit history. Young drivers and new drivers pay much more.
With no US driving history
You may be treated like a new driver, so prices can be high at first.
Get quotes from several companies. Ask each one directly: "Do you count foreign driving experience?" Some do.
Bring a letter or record from your home insurer showing years without claims. Some insurers accept it.
Ask about discounts: good student, safe driving apps, paying in full, bundling with renters insurance.
Getting a US license soon often lowers the price.
Buying only the state minimum. A serious accident can cost far more than the minimum limits.
Not listing every driver in your home who uses the car.
Letting the policy lapse. A gap makes future insurance more expensive.
Lying about your address to get a cheaper price. Claims can be denied.