What do you do after defeating Giovanni in silph co fire red?

It depends on what you've already done but make sure you beat Sabrina, the Gym Leader there first. If you went to Fuchsia City already and beat Koga, the Gym Lleader there and you already got the HMs of Surf from within the Safari Zone and the HM of Strength by retrieving the Warden's teeth and giving them to him so you get the HM of Strength and you can now go to Cinnabar Island. You can either go get there by Surfing on the water south of Fuchsia City and head west or you could Fly to Pallet Town and Surf all the way south until you get to Cinnabar Island. Next you go into the Pokémon Mansion to find the key to the Cinnabar Gym.