Birmingham has a  number of train stations. the main station is Birmingham New St, It is served by many of the rail networks. You can travel around Birmingham from this station or you can travel to other destinations within the UK. In particular you can catch a Virgin Train and be in London within 1 and a half hours.

http://www.networkrail.co.uk/birmingham-new-street-station/departures-arrivals/

The city centre also has two other stations, Moor St and Snowhill.

People often assume that Birmingham International Train Station is located in the City Centre but in fact it is 14KM East by the airport and the National Exhibition Centre.