You carry car insurance specifically so that you will have the money to fix your car in case you are in an accident. But when that accident happens, you may find that the car insurance company is interested only in minimising your claim and giving you as little money as possible for your losses. You do not, however, have to accept that first offer. You can reject that offer and negotiate a more lucrative settlement.
Look up the value of your car if the vehicle was totalled in the accident. You can use sources such as the Kelley Blue Book (kbb.com) and Edmunds (edmunds.com) guides to determine the fair market value.
Obtain several estimates for the repair of the vehicle damaged in the accident. You may be required to get an estimate from a shop that the insurance company specifies, but you can also obtain estimates on your own.
Document any time you lost from work, and gather information on the wages you lost as a result. Use your pay stubs and earnings reports to determine the value of the time you lost from work as a result of the accident.
Write a letter to the car insurance company, formally rejecting its claim and making a counter offer. Submit copies of all your backup documentation, including repair estimates, fair market value reports and lost wage information. Make copies of all documentation before you submit it.
Contact the insurance adjuster after a week or two to discuss the status of your claim and the disposition of your counter offer. Be prepared to negotiate the settlement you want.