Boat trip around the Capri island allows you to visit the famous rock structures, grottos and especially the Blue Grotto.
There are 2-3 ways to do this tour:
Large boat from Sorrento (80-100 people) - not recommended at all, large boats can't get as close to Grotto as small boats
Small Boats from Sorrento - decent boats, but you end up wanting too much time travelling from Sorrento to Capri
Small boat tours from Capri - this is what this company runs and is pretty good. Boat takes about 20-25 people, and in 1.5-2 hours does the complete round of Capri island.
English speaking guide on board. Loud speaker available. Boat goes near or rather inside many grottos. Very picturesque tour! The tour obv includes the trip to Blue Grotto!
Another way to do the same is a private boat from Capri. More