You won't have to go through the process of arguing your case again.
First, you will file to confirm the Award to make it a judgment, you can then proceed with the widely known process of enforcing upon the judgment.
The process for filing this differs county-by-county, but no matter where it is, you will not have to re-litigate the merits of the case (i.e. present your evidence and arguments again).
Generally speaking, a Judge will take the Award amount on its face and confirm/enter judgment consistent with the Arbitrator's decision unless there is some major ethical, conflict of interest, or bias issue.
FairClaims is here to provide you with resources and general guidelines to make this an easier process for you. FairClaims support is here to help you if needed.