To get to Kvitsøy you need to take the large, comfortable car-ferry "Fjordveien". The trip from Mekjarvik in Randaberg takes only 30 minutes and the ferry departs 8 times a day. You will find the ferry timetable here.
If you travel without a car, you can take an express boat - either from Stavanger or from Mekjarvik in Randaberg. Check out the timetable here.