You have a number of choices for making the trip between Glasgow and Cambridge, bus, train or aeroplane. The bus is the least favourable option as it takes at least 10 hours and costs about the same a flight. Flying could be the cheapest option if you manage to book far enough in advance to get one of the best fares, but remember to add on another 20 GBP to your calculations for transport to and from the city centres. From the Buchanan Bus Station in Glasgow, it takes 10-11 hours to travel to Cambridge by coach, including a transfer in Birmingham or Milton Keynes. There are two buses per day plus an overnight service. A single ticket is 43 GBP or you can buy a return for 56.30 - 62.10 GBP.
After booking online, you will be issued with an e-ticket, which you need to print out and take with you, or an m-ticket, which is sent to your mobile phone. Otherwise you can get at ticket at the bus station.
There are two trains per hour, from Glasgow Queen Street or Glasgow Central stations. Choose your train carefully when you book as there are only a couple of trains a day that have one change of train, on most services you have to change twice (at Edinburgh Waverley and Peterborough) or even three times (Edinburgh Waverley, Stevenage and Letchworth).
The journey takes 5-7 hours. A single ticket costs around 86.50 GBP or you can get an off peak return for 108.30 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.
On arrival in Cambridge, it is a 15-minute walk to the town centre, or you can catch a taxi outside the station for around 5 GBP. There is also a bus that runs about every 10 minutes.
To walk, exit the station and continue along Station Road, which is directly in front of you. At the T-junction, turn right onto Hills Road, which takes you towards the city centre.
Easyjet flies from Glasgow Airport to Stansted. There are 2-5 flights per day, which will get you there in 1 hour 20 minutes. If you book well ahead you can get a single flight for 23 GBP, but you are more likely to pay between 50-110 GBP depending on the day and time you travel. Be careful there are a number of extra charges that can give you a nasty surprise. It costs 6 GBP to check one 20kg bag into the hold. Easyjet automatically add 5 GBP travel insurance unless you remove that option during the online booking process. They will also suggest you buy a Speedy Boarding pass for 7.50 GBP, but this is unnecessary.
From Glasgow Central Station take a train to Paisley Gilmour Street, and catch the Arriva bus service (66 or 300) one mile to the airport. If you buy a ticket to Glasgow Airport, it is valid on the train and the connecting bus. A single ticket is 2.75 GBP. Allow at least 40 minutes to get to the airport from central Glasgow. Check in at least 40 minutes before departure, and show your passport, otherwise you will be denied boarding. Easyjet do sell a limited selection of sandwiches and refreshments onboard, but you might prefer to take your own.
From Stansted Airport you can catch a train to Cambridge, which takes with 30 minutes or 60 minutes and costs 9 GBP single. There is also a coach that takes 50 minutes and cost 12 GBP one way. The airport bus station is right outside the terminal entrance and you can buy your ticket at the bus station or on the coach.
If you have a very early flight from Glasgow Airport or arrive late you may wish to spend a night at a hotel near the Airport. With prices from as little as 35 GBP per night (cheaper than Cambridge!) it is worth considering.