The most romantic way to get to the islands is on a Ferry. There are several operators that cover the Scottish islands.
You can reach Shetland and Orkney via a Northlink ferry from Aberdeen. Shetland is also available via a ferry from from Orkney. To get to Orkney, you could travel by Northlink ferry from the ferry terminals in Aberdeen (to Kirkwall) and Scrabster (to Stromness). Alternatively, you could travel to mainland Orkney by Pentland Ferries on the Gill´s Bay to St Margaret´s Hope route. Finally, John O´Groats passenger only ferries run from John O´Groats to South Ronaldsay on Orkney. There are inter-island ferries available here through Shetland council. There are also inter-island ferries available at Orkney Ferries for the Orkney islands. You can book Northlink ferries below through directferries.co.uk:
It is relatively easy to reach most of the inhabited Scottish islands. The main operator on the west coast of Scotland is Caledonian MacBrayne (universally known as Cal Mac). The main port is Oban, where Ferries sail to nearby islands such as Mull and Lismore as well as further away islands such as Barra or Tiree. if you are travelling around the Scottish islands, you will definitely be visiting Oban at some point.
For more information on Ferries to and from specific islands, please see the relevant island page.