There is a state organization named Rhode Island State Referee Committee (RISRC) that qualifies referees and operates the referee program in RI. So the first step is to go to their website which provides information on becoming a new referee. The steps involve taking a course from RISRC to become certified, entering the referee database for assignments, and notifying the WFFSC Referee Coordinator who currently is Bob Enright at email@example.com.
Once you are certified and in the system and on Bob's list then he will assign recreational games usually starting in U8 to get some experience. As the referee gains experience they will move to older age games and maybe eventually move to be assigned to competitive games.