The most convenient way to reach Barcelona from the USA and the UK is by air.

Barcelona is served by an international airport BCN, El Prat.

The airport is located 12 kilometres outside the city, to the south-west. Most European airlines, and many international ones, operate flights from its international terminal.

The airport has three terminals. International airlines operate from terminal A; domestic flights by IBERIA, Air Europa and Spanair operate from terminal B as do British Airways and Lufthansa flights. Terminal C is used by Iberia's Barcelona-Madrid air shuttle. Some US carriers fly only to Madrid and then tranfer passengers to another national flight to get to Barcelona

University page directions

Tips to go from the Airport to Barcelona:
There are several ways to go from the airport to Barcelona:
BUS: There are direct buses to Plaça d'Espanya and Plaça de Catalunya
There is also a city bus (line 106) that also goes to Plaça d'Espanya but stopping on its way. Cheap though.
You get the buses out of terminal B (You'll probably will come out from bagage claim there)

TRAIN: There used to be a train that left every 30 min at 13m past and 43m past. However, the line is being renovated. I have been told that there is a bus that takes you to the train stop of Prat de Llobregat and then you take the train to Barcelona, where you can get off at Sants, Passeeig de Gràcia or Plaça de Catalunya. You get to the Airport train station from an elevated corridor in between terminal A and B. Update (mid-March): the train is now running (but not always) from the airport to the Prat the Llobregat station every 20min. There you have to tranfer to another train to get into Barcelona.

TAXI: It should cost approx 15-20 € to get to central locations in Barcelona coming from the airport. It is not a long ride. If there is no traffic, it is quick.

CAR RENTAL: I ignore details about car rental. You can take a look at the official airport page, where you can find the usual companies: AVIS, Europcar, Hertz, NATIONAL/Atesa. You can also use your favourite web travel searcher to look for good deals. I have found prices starting from 120 euros up for four days (May 17-21) (in principle covering insuranse and taxes and unlimited milage but this may be restricted to Spanish driving licence holders. In fact, I do not know).

Public transportation is the most convenient way to get around the Barcelona Metropolitan Area. All the Barcelona area shares a common way of paying fares at buses, metro (subway/underground) and trains. You can find maps here.
The metropolitan area is divided in zones. when you travel within a zone you pay a 1 zone fare if you cross 1 zone you pay a 2-zone fare, etc.
Within Barcelona (including airport) you are in the same zone, so you pay a 1-zone fare. If you come to the Universitat Autònoma (UAB) from Barcelona you cross 1 zone and you pay a 2-zone fare.
Current fares are:

	1 zone	2 zones
Single ticket	1.20 €	1.75 €
ten-ride (T10) ticket	6.65 €	13.30 €

Tranfers within 1h15m are consider the same ride in one zone (1h30m in 2 zones), so when you pass the ticket through the validating machine it will not charge you again.
So as long as you travel more than 5 times it is cheaper and more convinient the ten-ride ticket (T-10)
You can get the tickets from vending machines at metro stations. (and pobbably from bus drivers) But I doubt there are vending machines at the airport.