Get an attorney. It may be difficult in the current climate, when insurance companies are spending a good deal of money making insurance settlement suits near impossible to win, but you want a lawyer who can work with you during this process. Be sure that you communicate every directive to your attorney in writing.
Know your rights. Read through your state's information about insurance company liability to determine whether you have a legitimate complaint.
Gather all of the needed documents. Get copies of the police report as well as all information related to your policy and this specific case. You need to use these documents to begin to build a case against the insurance company. If you have not already done so, begin to document everything related to the case, including any telephone calls or electronic communications.
Write a letter to the insurance company. Outline your position and why you wish to appeal the settlement. Your attorney should be able to assist with the preparation in this letter. The most important points are not to claim responsibility in any way for the accident and to lay out your position clearly and succinctly. The letter is your best effort initially to make an appeal claim. In some cases, the company may reconsider after reading your letter, but in most instances, sending the letter is a formality. Your appeal will continue after you receive a response to your letter.
Consider hiring specialists. You can find professionals who will reconstruct accidents for you, and these people can help present your case to the insurance company. If your professional finds that you were not at fault or that the insurance company's version of the accident is somehow wrong, then you may be able to convince the company at this point in your appeal that offering you a better settlement is the way to go.