What is the way to captains quarters on Pokemon fire red while board SS Anne in Vermilion city?

You can't access the Captain's Quarters on the S.S. Anne in Pokemon Fire Red. The Captain's Quarters are only accessible in Pokemon Yellow, and they are the location where you can find the elusive Mr. Fuji.

In Fire Red, the S.S. Anne serves as a way to travel to Cinnabar Island. It's not a location with any particular secrets or challenges, and you don't need to do anything special to access the areas that are open.