Don't give a statement without getting advice from a lawyer about your specific case.
The general advice all lawyers give is "Don't give a statement to the insurance adjuster", and that's good advice. The problem is that thousands of people give statements to insurance adjusters every day - and most of them haven't spoken to a lawyer about their case. Although there may be general rules about what to do or not to do (like these), the kinds of things to worry about change from case to case. If you are going to go ahead and take the risk of giving a statement to an insurance adjuster without getting legal advice, read on.
Don't assume that "having nothing to hide" or that "telling the truth" will protect you.
No matter how truthful you may be, you should recognize that an insurance adjuster "for the other guy" has a job to do. That job is to develop facts that will allow the company to deny a claim, or develop facts that will help the insurance company minimize any damages they have to pay you. The insurance adjuster controls the interview, and the questions. No matter how honest you might be, there is always the risk of a question/answer that will be used against you.
Don't give the adjuster a statement the first time they call and use the additional time for case specific preparation.
The biggest mistake most consumers make is assuming they must give the adjuster a statement as soon as it is requested. Don't do that. The adjuster will be ready for the statement and have a game plan. You won't. Tell the adjuster it's not a good time for you and schedule a follow-up call for the statement. Using the extra time, prepare for the statement. This means reviewing the accident report, looking at the scene of the collision, pictures of the property damage, and any initial medical records you can get. If there are witnesses, call them. If there are other pieces of important evidence, check them out. Reviewing means more than glancing over, think carefully about the details.
Before the statement begins, insist on receiving a copy of the statement.
Most statements are recorded. You have a right to have a copy/transcript of any statement you give. Ask for it up front. If they say it isn't going to be typed up, ask for a digital copy of whatever they have (even if you don't know how to read the file with a computer).
Listen to the question, answer it, and don't volunteer information.
The worse statements (other when people lie) are when someone is nervous and talks too much, volunteering information that is unintentionally helpful to the other side. What should you do? Listen to the question; don't interrupt. Think about what the question is asking you and answer that question. After you have answered, stop talking and wait for the next question.