There is an excellent public transport planner for all forms of travel to and within Orkney is at Traveline Scotland.
There are three ferry companies that run to Orkney in the summer:-
The pedestrian only summer service from John O’Groats Ferries and two all year round daily passenger and car ferries – Pentland Ferries from Gills Bay to St Margaret’s Hope and Northlink Ferries from Scrabster to Stromness. Northlink also run a longer Aberdeen to Kirkwall service two or three times a week depending on the time of year.
If you’re flying to Orkney, flights can be booked on the Flybe website or you may want to book through flights if you’re coming from further afield.
Within Orkney, inter-island ferries are run by Orkney Ferries.
Flights within Orkney can only be booked by phone.