Doing business with your own insurance company after a car crash can be time-consuming and a hassle. Just imagine what it's like to deal with the insurance company of someone else who crashed into your car. Here are some tips to ensure you maintain your cool — and your sanity — when making a claim with the at-fault person's insurer.

The driver who crashes into your car is responsible for informing his or her insurance company about the incident. However, it's a good idea for you to call his or her insurer because motorists who cause accidents often may be reluctant reporters. So, it is important that you obtain the most complete insurance information from the at-fault person at the scene of the accident: insurance company name, claims phone number, address, and even the insurance agent's name.

Theory vs. reality
Auto insurance, in the simplest terms, is a contract between a motorist and a company in which the company agrees to pay for damages or losses its insured motorist causes. If a motorist damages your car and injures you, his or her auto insurer is responsible for paying you for your damages and injuries. Theoretically, all you should have to do is notify the other party's insurer of your damages and injuries, take the car to a body shop, go to the doctor, and expect the insurer to pay your bills.

Theories are not always put into practice, however. Insurance companies often say you must obtain their authorization to go ahead with vehicle repairs and injury treatments. Taking matters into your own hands can create a payment problem down the road if the insurance company claims adjuster says, "I didn't authorize that." So at least get the insurance company to accept liability before going ahead with repairs. You'll want to get the authorization in writing, so ask the insurer to fax it to you in order to expedite the repairs.

Pick your battles
Another person's insurer also might say you need to seek payment from your own insurer because it has no evidence of its policyholder's fault. This is why it's a good idea to notify your insurer immediately after the crash. Although most states have made it illegal for insurers to deny claims without reasonably investigating the facts, or to deny claims when its liability is reasonably clear, you might not be interested in fighting the other person's insurance company.

Hiring a lawyer if you decide to take on the at-fault driver's insurer may be a good idea, especially if you've been seriously injured. (Read When to hire a personal injury lawyer for more on that.) An attorney can help you navigate the sometimes-murky laws that govern insurance. But keep in mind that if you hire an attorney, he or she will take a cut of the settlement he or she helps secure.

When the other driver lies
You might have evidence of the other driver's fault — they may even have admitted it at the scene — yet find your claim denied by his insurance company. Why? Because he's told a version of how the accident happened that doesn't square with yours, and his insurer is standing behind that story all the way in order to avoid paying your claim.

"It happens all the time," says Texas attorney James Holmes. "Remember, the company's first impulse is to say 'no'. The insurance company will wholeheartedly adopt its policyholder's position."

This is especially common in cases where no police accident report was made, showing the importance of calling the police to the scene of any accident. In many states, if an officer at an accident scene determines the damage is minimal (usually less than $500), he will not make an accident report. Body shop estimates for that same accident, however, might run into the thousands of dollars. What now?

"You can't make the police officer write a report," says Holmes. "The best advice in that scenario is to do the officer's job by getting witnesses and all the information from the other driver. Then, get that car to a repair shop immediately, so you can minimize any questions about what caused the damage."