Filing the Complaint. A civil court lawsuit starts when you -- the "plaintiff" -- file your initial document, usually called a "Complaint." This document lays out every element of the case you are making against the other driver. You'll fully identify the parties involved in the case, state the facts on which your allegations are based, and then lay out and support the element of each of your claims. Each claim is usually referred to as a "cause of action." For example, in a typical car accident lawsuit, the plaintiff may bring separate causes of action for negligence, pain and suffering, and negligent infliction of emotional distress. Your Complaint will also typically ask for a certain dollar amount as compensation for damages (sometimes called a "Prayer for Relief").
There will be a filing fee that varies by state (and sometimes by courts within each state). You can probably expect a filing fee from under $100 to more than $300 for a civil complaint over a car accident. And keep in mind that if you win your case, the amount of the filing fee may be added to your judgment, so the other side may need to reimburse you for those costs.
Process and Service. After the court clerk creates the court file for your case, he or she prepares "process," the papers that have to be served on the person you are suing -- called the "defendant." Process includes a copy of your Complaint and a Summons requiring the defendant to answer your case within a specific period of time, usually about a month. This process must be delivered to the defendant. This is called "service of process." Each state has its own rules and procedures for how process must be served. Generally, the safest thing to do is hire the local Sheriff or Constable to serve process on the defendant. There will be a small charge, but again, if you win your case, the amount that you pay will probably be added to the judgment that you receive.
Defendant's Answer. After your Complaint is served on the defendant, the defendant must file a response, usually called an "Answer." In this Answer, the defendant raises all legal defenses that he or she has in response to the allegations you made in your Complaint. Don't be surprised if the Answer includes defenses that you think are ridiculous and bear no relationship to your case. Normally, defenses that are not included in the Answer are waived, so defense lawyers typically raise every defense under the proverbial sun, even if they don't seem to apply to the case.
Once the initial documents have been filed in a lawsuit over a car accident, the case proceeds to the discovery phase, where the two sides exchange information in a back-and-forth process that includes written questions and answers (interrogatories), face-to-face questioning in which answers are provided under oath (depositions), and requests for documents (including the medical records that detail your car accident injuries). Don't forget that informal settlement negotiations will probably be going on while the court-based lawsuit process is taking place, so your car accident case could get resolved at any time.