It's all explained in Supercarrier manual, p.58 for Case III recovery. The order is shortly:
Inbound - The first radio contact
Established - Once you are at the directed altitude and within xx miles of the marshal stack
Commencing - When you reach the assigned push time and departing the holding stack
Check IN - Control will be transferred from marshal to approach, and you must check in with the new controller
Platform - At 5,000 feet AGL you will select ‘PLATFORM’
Good tutorial explaining this