The quickest is probably to fly - various airlines such as BMI, BA, Easyjet all fly direct.
You could get the coach : http://www.nationalexpress.com/coach/index.cfm
Or you could get the train - either the overnight sleeper or the regular day train :http://www.scotrail.co.uk/caledoniansleeper/timetables.html or http://www.nationalrail.co.uk/
Personally, if I had the choice, I would do the train/sleeper train. By the time you have checked in for your plane, flown for an hour and then got from the airport to wherever you want to go, you could probably have almost done the journey on the train, and with the train, you get to see much more. I think the overnight train is romantic!
For cost wise, probably the bus is the cheapest option, followed by a plane ticket if you book enough in advance. about 10 years ago
If you're on a budget take a coach.
Try out http://www.nationalexpress.com/coach/index.cfm or http://mobile.usablenet.com/mt/us.megabus.com?un_jtt_redirect if money's tight. I took a 9 and a half hour night bus from Glasgow to London..it wasn't the most comfortable trip but it was cheap and I got there around 8am so I had the whole day in the city. almost 10 years ago