Unless you have your own boat or plane, the only way in is on one of the Calmac ferries:
By ship
Calmac (http://www.calmac.co.uk/) run 3 ferries connecting Mull with the mainland, and one to Iona.
Oban to Craignure daily 5-8 times per day, takes 45 minutes. Probably the most convenient for those without a car, as Oban has good bus and rail links. The ferries are timed to meet with the trains to and from Glasgow.
Lochaline to Fishnish Is the quickest taking 15 minutes, on average and the cheapest option, although the timetable is quite sporadic. Note that Lochaline is in a very remote location and the drive there is mostly single track, and a rather torturous 40 miles from Fort William. Consider this option only if you are travelling to Mull from the North.
Kilchoan on Ardnamurchan to Tobermory. Three per day, taking 35 minutes. Given how remote Ardnamurchan is, this is more a way of getting there, than a way of getting to Mull.
Iona to Fionnphort about 9 per day, taking 10 minutes. During peak summer season, the ferry runs on demand and will make as many crossings as necessary.