There are various ways of getting to the city:

By Aerobus (coach)
The stops for the Aerobus are right outside the terminals (A, B and C).
One coach leaves every 12 minutes. You can get off at various points in the
centre of Barcelona (it will take about 30 minutes):
Sants Station, where you can change to undergrounds lines 3 or 5.
Plaça d'España, where you can change to undergrounds lines 1 or 3.
Plaça de Catalunya, where you can change to undergrounds lines 1 or 3.
Passeig de Gràcia, where you can change to undergrounds lines 2, 3 or 4.

By Train
The prices of tickets vary depending on the zones through which you travel.
To get from the Airport to the Centre of Barcelona you travel through 4 zones, the cost
of the ticket is 2,40 Euros. All trains leaving the station go to the Centre.
Timetables: From the Airport to the Centre of Barcelona the first train leaves
at 6 a.m and the last at 10:29 p.m. A train leaves every 30 minutes and it will
take you about 35 minutes.
Important: Do not throw your ticket away after validating it because you will need
it to leave the station on reaching your destination:
Sants Station, where you can change to undergrounds lines 3 or 5.
Passeig de Gràcia, where you can change to undergrounds lines 2, 3 or 4.

By Taxi The cost to the Centre of Barcelona is around 30 Euro and it takes about 25 minutes.

Hire car There are several car hire companies at the airport


PUBLIC TRANSPORT
In Barcelona city there's an Integrated Tariff System and the cheapest
way to travel by public transport (either bus or underground) is getting a
travel card. You can get a T-10 card, it allows 10 combined journeys in any
means of transport. It costs 6,65 Euro and you can use the same ticket
during 1 h 15' once validated. You can acquire the cards at the Metro Tickets
Offices and Automatic Machines and at the "Tabacs" shops. More information
is available on http://www.tmb.net/en_US/barcelona/moute/targetes/targetes.jsp