Insurance has a unique vocabulary, so I'll go through a bit of definitions just in case:
Premiums: the cost of the insurance in dollars, usually paid every 6 months.
Liabilty: insurance that pays the other guy in an accident that is your fault (both property and medical)
[keep in mind, if the accident is NOT your fault, the *other guy's* liability insurance pays for *your* medical and property damage]
Collision: insurance that pays to fix your car in an accident that is your fault
Comprehensive: insurance that pays to fix your car when non-accident damages occurs to it (inclement weather, vandalism, etc.)
Medical: insurance that pays your (and your passengers) doctor bills in an accident that is your fault.
Uninsured/Underinsured: Insurance to cover you and your car and passengers in the event you get hit by someone with no insurance, or with too little insurance coverage to pay for all the damages you sustain.
Emergency Road Service: Insurance that pays for a tow truck if your car breaks down and you call a tow truck company. Just get a receipt from the tow truck driver and turn it in to your insurance agent. This insurance is like $1.50 month. Well worth it if you drive 15 year old cars in arctic climates like I do.
Deductible: the amount of dollars you pay toward an accident before your insurance kicks in. Usually $250, $500, or $1000. The higher your deductible, the more risk you assume from your own pocket, but the less your Premiums are.
With Liability, you'll also see numbers like these thrown around: 100/300/50. That means that your Liability insurance will pay up to $100,000 per victim, $300,000 per accident, and up to $50,000 for property damage. Those values will not be exceeded. So if you hit a Hummer with 8 people in it and they all perish, your 100/300/50 insurance is going to be exceeded. Technically, you owe the rest out of your pocket (these numbers are pretty unlikely to be exceeded, though). The State mandates how much Liability insurance you must carry, and by that, I mean how big those numbers separated by slashes have to be.
If you have a cruddy little $2000 car that you back and forth to work in, don't bother carrying comprehensive or collission insurance. That is just personal advice. You'll kick me if you take my advice and then the next day after buying liability insurance you fall asleep at the wheel and ditch your car. But generally, don't pay and pay and pay for insurance when you could just put the money saved by buying just liability insurance in a savings account and buy another $2000 car if you wreck the one you're driving.
If you buy a new car on payments, the bank will require you to carry a sh!tload of insurance, in all the categories mentioned above. They don't want you to wreck the car, quit paying for it, and then they repossess a hunk of junk.
File a Claim: There has been an accident in which your insurance will need to pay someone/you. You call your insurance agent and file a claim. They conduct a routine investigation, and maybe hire a claims adjustor to calculate the damages. They send someone/you a check for the damages minus the deductible.
Damages: the cost in dollars of the medical bills and property loss.
Proof of Insurance: usually a litttle card with some information on it about your vehicle, you, and your insurance company and the date that your current policy expires. The police often ask for this when you are pulled over. Carry one in your wallet and put the other on in your car.
Insurance Policy: a really long document on thin folded paper that tells in excruciating detail the terms and conditions of your coverage. (covered damages = they pay, uncovered damages = they don't pay). The small print. Here you find out whether or not your collision coverage includes damage from earthquakes, terrorists, war, nuclear accidents, suicide attempts, blah blah blah blah.
Another thing to know about insurance companies: Their financial goal, their reason for existence, is to NOT pay the claims filed against them. If your insurance expires on 5/28/2004, It expires at 12:01AM on 5/28/2004. Get in an accident on the way to work at 7:30AM on 5/28/2004, and they will not pay a dime. Delivering pizza for a living? Get into an accident? Sorry. You're on your own. They get out of every claim that they can.
Discounts: Circumstances that result in a reduced premium: accident free (takes a few years on a policy to get this), good student, airbags, antitheft devices, married, shorter than average drive distance to work, multiple policies with the same company, being a female.
Totaling: Another important concept is the Blue Book value (or equivalent) of your vehicle and the notion of "Totaling" a vehicle. A vehicle is "totaled" when the amount of money it would take to fix it exceeds the Blue Book value. In that case, the insurance company declares the car totaled, and gives you a check for the blue book value, minus the deductible (assuming it was your fault). Since the insurance company doesn't really want to own the car, sometimes the owner elects to buy it back from them, and they generally sell it for just a few hundred dollars just to get rid of it. The owner may be able to keep driving the car as it is, or do some repairs or whatever. Depends on what kind of damage it sustained, and how low the blue book value was.
Like my 1990 Plymouth Sundance probably has a Blue Book value of like $1500. So a fender bender accident could leave my vehicle totaled, because body work is expensive. Let's assume it was the other guy's fault. I get a check from his insurance company for the blue book value. Then I keep driving my wrinkly car around, because what do I care?
Anyway, this is a good start. Buy only the insurance that you need. Don't buy medical coverage through your car insurance if you already have good health insurance (unless you constantly carry passengers have no health insurance, I suppose). Don't buy collision or comprehensive insurance on your $500 unrestored 1972 VW Beetle. Tell your insurance agent about all of the discounts that apply to you (they don't volunteer these discounts, sometimes). When you turn 25, tell them that too. It's another discount I forgot to mention.