There is a bus service running in coordination with the arrival of flights into Girona that will take you into Barcelona. They make one stop at the BARCELONA-NORD Bus Terminal.
The price is around 15 € per person and the journey takes about 1h 30 min.
After you reach the bus terminal, you can take a taxi or the Metro (it is very close) from the ARC DE TRIOMF station, which is the red Line 1. In PLAZA CATALUNYA, switch to the green line 3 and go to the FONTANA station.