I got this information from the following site:
Airwise.com Taxi
Journey time from central Barcelona is around 20-30 minutes.
Fare: Between EUR€15 and EUR€25 depending on destination.
Train
Train services to the airport are available every 30 minutes from Clot-Arago, Arc de Triomf, Placa Catalunya and Barcelona Sants stations.
Services operate 05:30 - 22:11.
Journey times from: Clot-Arago 31 mins, Arc de Triomf 27 mins, Placa Catalunya 25 mins and Barcelona Sants 20 mins.
Fare: EUR€2.
The airport station is connected to the terminals by moving walkways.
Information is available on Tel: 902 24 02 02.
I used the train in May and found it very convenient as long as you do not have too much luggage. I believe the fare was 2,20 euros, because when I asked the price at the booth, the man just held up a sign with 2,20 on it. He must get asked that question over and over so it is easier to just hold up his sign.