You can travel to the island by plane and ferry.
Loganair operates regular flights from Glasgow International Airport and Edinburgh Airport.
Calmac operates several ferries per day from Kennacraig to either Port Askaig or Port Ellen. (NB - From Port Askaig, you can also jump on board the small ferry to visit Jura.)
Citylink operates a connecting bus service from Kennacraig to Glasgow Buchanan Street bus station.