Number of ways...
If you want a bargain way to get the Barcelona and not too concern about the level of service or comfort...
Try FlyGobeSpan.com which will be flying daily between JFK
and from there book a seat with a low cost carrier...
Ryanair can fly you from Liverpool - Barcelona/Gerona for about £20 each way or if you want to fly to Barcelona's main airport easyJet fly to BCN
for about £35 each way. As both airlines have hubs at Liverpool.
Flights with FlyGlobeSpan are about £120 each way including taxes even during the summer!
If you want business class accross the Atlantic try SilverJet between EWR
for about £799 return (inc tax) and book flights from LTN
on to Barcelona with Ryanair or Easyjet as both again have hubs at LTN