There is a shipping company Tirrenia that provides connection by ferries between Naples and Caliari in Sardinia two times a week.
On June 2016 ferries leave Naples at 19.00. From Caliari to Naples ferries leave at 19.00 as well. Average journey time is 13 h. 30 min. Average one way ticket price for a person on June 2016 starts from 35 EROUS. Ferry prices vary a lot depending on the season and when you book them. Also prices depend on the way of travelling on ferries: cabin/CABINA USO ESCLUSIVO, single bed/LETTO SINGOLO, seats/POLTRONA or bridge/PONTE. As usual the option ponte is the cheapest one. If you want to take with you animals or additional equipment such as cars, bicycles, motorbikes, it will cost additional amount of money.
You can buy tickets and look at the prices on the official Tirrenia web site.
*Attention: the timetable is approximate. It changes and varies a lot. Therefore, it is higly recommended to check the timetable on the official Tirrenia web site before buying tickets.
About other connection with Sardinia you can read here: Sardinia: how to reach?