Between Glasgow and Edinburgh you have the choice of travelling by train or by bus. The bus is cheaper, but the train is up to 25 minutes faster. If you wish to take the bus, you can board a Megabus at Glasgow's Buchanan Bus Station, it takes 1 hour 15 minutes to travel to Edinburgh and they depart every 15 minutes at peak times and the first bus departs at 5:20 AM and the last bus leaves at 11:30 PM. A single ticket is 3.50 GBP or you can buy a return for 7.00 GBP.
Once you’ have booked, you will be issued with a reservation number that you need to show to the driver before you board. You can also get this number sent by text to your mobile phone for a small fee. You can change your Megabus ticket up to 24 hours ahead of your scheduled travel date for a 1 GBP fee plus any difference in ticket price.
There are four trains per hour, from Glasgow Queen Street station. The journey takes 50 minutes (25 minutes faster than a bus between Glasgow and Edinburgh). A single ticket costs around 10 GBP or you can get an off peak return for 10.30 GBP.
The UK train ticketing system is notoriously complicated. It is usually cheaper to buy your tickets up to 6pm on the day before you travel than on the day. And fares are more expensive if you travel before 09:30. You get the best fares by booking up to three months in advance. You can buy your tickets online, at the station ticket counter, or from the ticket machines on the main concourse. If you book online you will need to collect your tickets from the ticket machine using the same credit card you used to book your tickets online.