How do I go about being in a car accident while in a uber/lyft?

Your only option is to sue the driver: Uber or Lyft are not liable for the accidents their drivers get into generally, since those drivers are generally independent contractors, not employees. You sue the driver the same way you would sue any other person who injured you with a car: you file a summons and complaint and serve it on the person. You can recover medical bills (ones not paid by your insurance or Medicaid/Care), lost wages due to the accident (if any), and, for serious accidents which result in significant and long-lasting impairment or disability, some amount for "pain and suffering." Note, however, that you will need medical expert (e.g. doctor) testimony to recover any amount for pain and suffering and for  any but the most obvious and directly linked to the accident--as well as comparatively modest--medical bills. (I.e. if you went to the ER to get checked out, you can generally get that bill without medical testimony, but would need medical testimony to recover for therapy, surgery, chiropractice, etc.) Therefore, unless you are talking many thousands of dollars or serious disability/impairment, this may not be worth doing, since medical experts are expensive: for a small or even medium amount of money, you could spend as much or more on the case as you will get back. If you did incur large bills or disability/impairment, speak with a personal injury attorney (many provide a free initial consultation: you can ask about this before making the appointment) about your case.