In order to give a complete answer, it would be helpful to know whether or not there were personal injuries involved, and the state in which the defendant (the person being sued) lives, or where the collision occurred. One of those locations would be the proper place for suit.
If you sustained bodily injury, you are not advised to handle the matter yourself. This is because even if fault for the collision is clear ("negligence"), proving damages (the amount of money to which you are or feel you are entitled) can be complex. For example, the medical professionals by whom you were treated would have to be subpoenaed to testify, you would be subject to depositions, and generally, it is hard to be objective about your own case. If the defendant was insured, his/her insurer would appoint an attorney to defend him/her, so if you do not have one, you may be outgunned.
If property damage alone is involved, you may be able to handle the matter yourself, altho it can still be complex. In either case, you would need to prove that the person who is being sued was negligent. Negligence means that the other person did not use that degree of care that a hypothetical "reasonable person" would have used under the same circumstances. Factors such as violation of the traffic law may be relevant, but the fact that someone was issued a ticket is not determinative, and may not even be admissible into evidence unless there was a conviction on the ticket or the person pled guilty.
There is more to this, such as the mechanics of actually filing and serving (delivering) the suit, but this should get you off to a good start.