How to get from the airport to the city center by train or bus.
Take the Aerobus. You can pay the driver (cash only) or buy tickets from vending machine.
http://www.aerobusbcn.com/
Mary is correct. Take the airport bus. It will drop you off at Placa Catalunya and from there you can get to where you are staying either by foot or Metro. The machine next to the bus stop takes American credit cards (i.e. without chip and pin).
Aerobus is 5.90 euro per person.
Taxi is approx 20 euro to Placa Catalunya.
Convenience may be worth a few extra euros if there are 2 of you.
(By the way it is "el Prat")