The timetables for boats and buses can be found on Snelandia.no. Fill in where you want to travel from and to, and which date. If you press search without filling anything in you will get a map of the area with the harbors marked.
Hammerfest have boat connection to Alta, Sørøya, Seiland, Havøysund and Rolvsøya.
Tickets can be bought on Snelandias mobile app, or directly on the boat. It is not possible to book in advance.