Leaving the camping, walking 300 meters to the left, you'll find a train station similar to a metro station with a train every 10 minutes from monday to friday. Weekends there's a train every 15 minutes. (1st train at 5:12AM, last train at 00:00)
The best station to stop and visit Barcelona is 'Plaça Catalunya'. There is connection with other metro lines and bus from Plaza Catalunya. Once you arrive you can visit Passeig de Gràcia and Las Ramblas.
Once you want to go back to the camping, just go to Plaza Catalunya again and jump in the train (Renfe) towards Mataró or Blanes and stop in El Masnou
Beside Plaza Catalunya there is a night-bus stop. There is a bus every 45 minutes between 1AM to 5AM and the bus code is N-80 y N-81. Buses stop in the Masnou station, not far away from the camping gate.