There're trains every 15 to 20 minutes from Edinburgh to Glasgow at 8 GBP return. The journey takes about 50 minutes.
There's a discount for three people travelling together. The discounted price goes down to 5 GBP return.
TRAIN: I travelled to Glasgow the first time with ScotRail. I already had a Britrail pass and decided to take the Caledonian Sleeper so I wouldn't waste daylight travelling. It only cost an extra £27 for the sleeper. You board the train at Euston station in London around 11pm, check in with the Porter, he shows you to your compartment and asks what you want with your breakfast in the morning. It's a continental breakfast but it's brought right to your door! I was lucky and ended up with a compartment to myself. There are singles and twins available. And they are tiny so I was really glad not to have to share it. I managed to get about 6 hours sleep before I got off the train at Glasgow's Central station. You don't have to get off it right when you arrive though, they let you stay on till around 7 or 8am.
I then walked to Queen St. Station to catch my next train to Oban. There is a shuttle but I decided to walk.
When I went back to London I took the First Class train back. Virgin Rail's First Class is excellent. I originally was booked on the sleeper for the previous evening but my plans changed and I spent another night on the west coast. At Queen St. I took the shuttle, and checked how much extra for first class. Only £29 so I went for it. It was well worth it. It's a 5 hour ride (approx) and I really enjoyed the trip. Big, comfy seats, the food and alcohol are included and the guys serving in my car were hilarious. They kept filling up my wine glass even when I laughingly protested! And a lot of food to choose from. I'd definitely do it again.
For more info click here: ScotRail
PLANE:I've also flown into Glasgow airport which is a major international one so many carriers fly here. It's easy to get around. It's not too big so that makes it nice. The only problem I had was that my suitcase arrived damaged. But the airline people gave me all the proper forms so I could be reimbursed when I got it fixed. It's easy to get out of if you have a car. My (then) boyfriend picked me up and we were out in no time.
I got to and from Glasgow by train. I stayed in Scotland for a month so I travelled to Glasgow every now and then.
Because I took the train I didn't know what the traffic was like. To me it seemed as though there was no parking in downtown Glasgow so if you can, take a cab or the bus to get around.
A car is a really convenient way to get around, but you can arrive by train from London within a matter of hours.