Lawyers are typically paid in one of three ways: flat fee, hourly, or contingent. Most personally injury claims are handled by lawyers on a contingent fee basis. This means that you will not have to pay anything to the lawyer unless and until they are able to recover something from the insurance company on your behalf. Once they obtain a recovery, either through settlement or trial or arbitration, they typically collect one-third of the amount, plus any expenses they have advanced to you for things like filing the lawsuit, deposition transcripts and medical records.
In some cases the court will order your attorneys’ fees to be paid by the other party. You should speak to your attorney about this possibility.
If you are forced to file a lawsuit against the at-fault driver, their insurance company will hire a lawyer to defend them. That lawyer will be paid by the insurance company.