It is worth visiting the Orkney Travel Timetables website to find out the latest times and routes to and within Orkney.
Northlink Ferries: between Scrabster on the Scottish mainland and Stromness in Orkney. There is usually at least one crossing every day taking less than 2 hours.
Pentland Ferries: between Caithness on the Scottish mainland and St Margaret's Hope in Orkney - 1 hour. From there it is around 30 minutes drive into Kirkwall.
John O'Groats Ferries (summer only): foot passenger ferry from John O'Groats to Burwick in Orkney.
It is possible to fly from Glasgow, Edinburgh, Inverness and Aberdeen to Kirkwall Airport.
There is a regular ferry from Kirkwall to Shapinsay (the Ro-Ro ferry MV Shapinsay), see ferry timetable here.