Explore the S.S. Anne thoroughly. It's a multi-deck ship filled with many trainers, including Gentlemen, Sailors, and Chefs. This is an excellent opportunity to gain experience and money. heal your Pokémon at the beds in the cabins if needed.
On the top deck, you'll encounter your rival, Blue, for another battle. His team will be stronger, so be prepared. After defeating him, head to the Captain's cabin. The Captain is seasick, and after you rub his back, he'll reward you with HM01 (Cut). This Hidden Machine allows a Pokémon to learn the move 'Cut', which can be used outside of battle to clear small trees blocking paths. Teach 'Cut' to a Pokémon you don't plan on using in battle, like a Farfetch'd (obtained by trading a Spearow in Vermilion City).