There's one sure-fire way to make your insurance cost more: Get in an accident. For a teen driver, the best way to keep those rates low is to be a good, attentive and safe driver. Anything that results in a claim on your insurance is going to drive up the premiums, erase any "good customer" discounts and cost you a lot of money in the long run. We're not just talking about serious accidents, either (which, obviously, are to be avoided). Any fender-bender or parking lot bump will increase insurance rates.
Don't think you're in the clear just because you didn't cause the accident, either. Speeding tickets, getting busted for rolling a stop sign, reckless driving and other moving violations will impact your driving record and leave you with points that represent an increase in insurance rates. Get caught driving drunk and the penalties are even worse, including fines and possible revocation of your driver's license.