Getting around Barcelona is very easy.
From the airport, for example, the preferred option is the Aerobus, which offers a fast (35-minute) and very economical transfer to the city center, that is, to Plaça de Catalunya.
Once in the city, you can use the Hola Card, which offers unlimited access to all public transport in the city for 48, 72, or 120 hours. This pass includes the metro, buses (TMB), the urban train (FGC, Zone 1), the Montjuïc funicular, the tram (TRAM), and regional trains (Rodalies de Catalunya). You can also simply buy metro tickets at any metro station.
Finally, to discover the main tourist attractions during your stay, the open-top hop-on hop-off is the ideal way to explore the city at your own pace.