Trains in Spain are quite reliable, fast and relatively cheap. The main train station in Barcelona is Sants. You can get there via Metro line 3 and line 5. Most international trains from Barcelona leave from Sants and there is also local & tourist information centre.
Barcelona’s other main station is Estacion de França. Some international trains go from here and you can reach it by metro to the nearby stations of Barceloneta or Jaume I. You can find timetables of all trains to Barcelona and from Barcelona on http://www.renfe.es
Trains to other parts of Catalunya and Spain also stop at other urban stations, including Plaza Catalunya, Passeig de Gracia and Clot. They might be more convenient than Sants station, and the queue for tickets will certainly be smaller.