train from edinburgh tp glasgow

There is no railway station at Edinburgh Airport, so you will need to get to Edinburgh Waverley, which is in the city centre. Options for doing that can be found on this airport webpage: http://www.edinburghairport.com/transport-and-directions/trains Note what it says in the section headed 'Travelling onwards by rail', specifically about a combined bus and train ticket which you can purchase from a machine in the airport arrivals area. I haven't use that, but I wouldn't be surprised if you need a chip & pin debit or credit card. Trains from Edinburgh Waverley to Glasgow Queen Street run several times per hour, even at that time of the evening, and it takes 50 minutes. There are slower services to and from Glasgow Central. See www.nationalrail.co.uk and use the journey planner to see your options. A single off-peak ticket is £12.50, and there is no need to book in advance.

Edinburgh airport has a direct coach every half an hour from Buchanan St Bus Station. £10 single.

Marco makes a good suggestion, but note that those coach services are only every 30 minutes until 19.30 and hourly after that until the last departure of the evening at 22.30. If that fits in with your itinerary then it's easier than going into Edinburgh to catch the train, but coaches can and do sell out so it would be wise to book at http://www.citylink.co.uk/

Yes I didn't notice the intended departure time - but I am sure they would be a lot more convenient and quicker than going in and out of Edinburgh. There has always been bus services to Edinburgh airport from Glasgow, but this dedicated service is new. Not sure whether the OP intends to return to Glasgow or go to Edinburgh from the airport on 2 Sept - again for the moment bus is the best public transport in the second case. If going back to Glasgow the return fare is £13 if booked in advance.