Just bring along your sun cream, sunglasses, a hat, and your swimming costume.
Your private skipper will be waiting for you a the port of Marina Grande in Sorrento. An operator will be waiting for you at the marina grande pier with a sign with the name of the company written on it. You will also receive a photo of the boat to recognise it.
In the next 7/8h you will enjoy a staggering amount of scenic landscapes, from Sorrento peninsula to Capri. Your private skipper will show you all the best places to take pictures, relax, and snorkel.
You will see the main seaside landmarks of Capri: the White Grotto, the Red Grotto (or Grotta Corallo), the Faraglioni. You will also have 3/4h to visit the beauties of the island on foot and go shopping. Always ask your skipper for some advice on where to go for lunch, he wll help you.
Afterwards, your boat will take you to Capri's most famous grotto the Blue Grotto. If you choose to visit it, the entrance fee is 14€.
Then, you can relax on your way back to Sorrento.