There are several different ways of getting to the Scottish Islands. Probably the easiest way to get to the islands and especially the more remote islands is to fly there. Flybe and Loganair fly to quite a few of the Scottish islands.
The most romantic way to get to the Scotiish Islands is by Ferry. There are ferries from Aberdeen and from the far north of Scotland to Orkney and Shetland and ferries to the inner and outer hebrides from the west coast of Scotland (many from Oban).
It is also possible to travel around mainland Scotland (and the rest of the UK) on the Train. Some of the scenery on the train journeys around Scotland are magnificent. I recently went on a train from Fort William to Mallaig (on my way to Rum/Canna/Muck) and the journey was stunning. You can book a train around Scotland (and the UK) using the Trainline.