The two main railway station that serve Glasgow are Glasgow Central and Glasgow Queen Street. Trains from these stations run to many different major UK cities. There are also many amenities at Glasgow Central station including; toilets, baby changing facilities, showers, telephone, parking at Oswald Street, photobooths. Similarly Glasgow Queen Street has toilets, parking, payphone, waiting areas, public WIFI and refreshment facilities. 
London is one of these places, from London Euston train station to Glasgow Central it would take approximately 5 hours and 10 minutes, although it is important to note times may vary. There is around 34 trains per day and tickets costs vary from £70 - £200 depending what class you cant to travel in, how early you book, what time of day and if its a weekday or weekend.  
From Edinburgh Waverley train station to Glasgow queen street it would take approx. 50 mins, on a normal day there can be 172 trains per day and the average ticket price is around £13. From Aberdeen station to Glasgow queen street approx. 3 hrs and 30mis, with an average of 31 direct trains per day and £13 tickets. 
London Euston and Edinburgh Waverly have all the same facilities as Glasgow Central and Queen Street.
There are also various different train operators which serve Glasgow central and queen street these are Scot rail, cross country and virgin trains. You can see the routes these train operators do in the images below.

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