There are boat tour companies on the dock that run regularly. You can’t miss them. You just book on the spot. Typically it’s an hour around the island, with optional Blue Grotto stop. The Blue Grotto may not be open (depends on weather/sea levels.) I found the hour tour very enjoyable and a decent value even without Blue Grotto.
I did the same thing you are, and it’s a great way to fit Capri into your schedule. Just get on the earliest ferry you can. I think I got to Capri by around 8:30am, took a boat tour, and the dock was just starting to fill up. Capri Town was already crowded in the morning, but Anacapri was wonderfully free of tourists well into lunchtime. Go straight there. Take the chairlift up to Monte Solaro (a trip highlight). By 3:00 you’ll be ready to move on and Capri will be in full zoo mode.