You can either take a bus from one of the terminals (Terminal 1 I think) which will take you straight to the park. I'm not too sure on the details but it'll cost around 30€ for a return.
OR you can do it by train (which is what I did) and whilst there's more changes it's about half the cost of the bus. (And more regular as far as I know.)
1. Take the rail service from Terminal 2 to Barcelona Sants station. (About 15 minutes and around 3-4€ return.)
2. At Barcelona-Sants you can buy a ticket to PortAventura station for around 15€ return. Spain has three types of rail transport, long-distance, medium-distance and short-distance. I believe you're looking for a
medium-distance train which will terminate at
Tortosa.
3. PortAventura station is pretty small and about a 20 minute walk away from the park gates/hotel resort. When you get there, make sure you make a note when trains will take you back to Barcelona-Sants because they're less regular and not every train stops at PA station.
You can find out more information at
http://www.renfe.com/EN/viajeros/horarios.html
Hope that's helped a bit and not too confusing, anything you're still unsure about let me know. I can't help you with the bus option much I'm afraid but I'd say getting the train is just as easy, cheaper and more comfortable.
