From the airport
Aerobus shuttle: Departs every 5-10 minutes from terminals 1 and 2, daily from 5:35 AM to 01:05 AM. Tickets can be purchased on the bus. For more information see here. Drops off at Plaça Espany and from there take the L3 subway ride to Les Corts.
Bus: Line A1 /Lines A2 to Pl Espanya stop. It's a 20 minutes trip. If you are in the city for a few days buy a T-10, Multi-person card for 10 journeys, (€10.20). It works on the metro too.