The claims process usually proceeds in predictable steps. Before you file a claim, you must notify people who may be responsible for the accident that you've been hurt and intend to file a claim for your injuries. This increases your chances of getting a quick settlement and prevents others from later saying that your claim unfairly surprised them.
Next, after you've taken time to thoroughly investigate your claim by gathering evidence, establishing who's responsible for the accident, determining what you believe your claim is worth, and planning good arguments, you will write a formal demand letter and submit it to the insurance company of the person who you believe is responsible for your injuries. (This may include your own insurance company -- for example, if you are covered by a no-fault automobile policy or need to make a claim for uninsured or underinsured motorist coverage.) From there, you will engage in informal negotiations with the insurance company until you agree on a settlement you can live with.
Many insurance claims are that simple, though sometimes you may find yourself dealing with a stubborn or unreasonable claims adjuster. If that's the case, you must resort to more determined negotiation tactics -- or perhaps consult an experienced personal injury lawyer. If all else fails, you may even have to take your case to court.