The most important thing to understand about insurance is that any claim has to be documented as completely as possible. Even if it appears that you have an airtight claim, make sure you can document it. If witnesses or expert testimony is available, record them. Get copies of police reports, damage assessments, medical reports, and any other official reports or documents.
Be honest with the adjuster or claims department. You do not have to go out of your way to provide extra information, but do not hold back. State your case simply and completely. Do not admit to any wrongdoing, even if you feel that you are at least partially responsible for the incident. If your insurance company is not comfortable with the information, they could use it against you to deny the claim.
If the claim is minor, it may be in your best interest to pay the costs out of pocket. Insurance companies are wary of writing policies for people who have a history of seemingly frivolous claims, so save the claim process for instances where you cannot afford to pay the costs. It may inconvenience you to pay out of pocket for a legitimate claim, but in the long run you may need to have the insurance company on your side for something major, and a list of small claims could actually work against you.
Some people think that the first thing they need to do is hire a lawyer to help move the claim along. Forget the idea. If you start talking about using lawyers, you may put the claim into jeopardy. Insurance companies have more resources than you do, and if you turn the claim into a legal battle, you have very little chance of winning. Save legal avenues as the last resort, and even then it is best if your attorney is the one who makes the insurance company aware that the situation has come to that.
You do not have to accept the first offer an adjuster makes. If you feel the offer is lower than the damage calls for, say so. If not, you can still negotiate with the company later, but not if you accept the adjuster's offer. It's okay to accept an offer that you feel is accurate, but don't feel pressured into accepting a settlement that is far too low to be a just payment on the injuries or damages.