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The conventional way is to travel from Glasgow to Oban (2 hours or so) and get the calmac ferry over, but if you're feeling romantic/rich, you can get a seaplane from Glasgow city centre (weather permitting). It goes daily (I think) and seats about 12.
Hi Greyvix, you are best advised to hire a car in Glasgow and drive to Oban. Oban is around a couple of hours drive from Glasgow through some incredible scenery . Plus a car will give you mobility on Mull which you really need, as getting the best out of Mull without a car is difficult to say the least. However there are trains to Oban out of Glasgow if you need to use the train, and probably coaches but it would be slower..although the train journey is also stunning.
I assume you've booked the ferry? If not, do so in advance as some sailings get booked up early particularly in July. Ferries are Here.
It's a heck of a long way to go for a weekend; I'd advise you to try to go for longer if you can, a week ideally, assuming that you are going for a break and sightseeing. The island is bigger than people realise, and getting around takes a lot of time as it is all windey slow single track roads.
Mull is a fantastic island and one of my favourite places. You'll love it
Don't forget to pack midge spray and your camera, and if you like wildlife take binoculars - Mull is packed with amazing wildlife.
Another way would be sleeper to Fort Willam, then hire car to Mull via the Corran Ferry then the Lochaline Ferry. Then you could come back on the Tobermory-Kilchoan ferry then back to Fort Willam via Ardnamurchan which is stunning. This avoids the busy and expensive Oban-mull ferry.
But I agree with whoever says a weekend is not long enough. Could you come up Thursday night and then back Sunday even?