Reus airport is a tiny airport located 108km far from Barcelona city, and the third airport in Catalonia, mainly used by travel agencies, charter flights operated by Thomas Cook or Thomson Airways. Ryanair, Jetairfly and Jet2 also operate from Reus airport regularly and the destinations are very limited, at the moment London Stansted and Eindhoven.
The airport is located in the surroundings of the city of Reus, 3km far from the south-east of the city and 13km far from Tarragona city. I wouldn't recommend you to fly from Reus since the transportation services to other parts of Catalonia are not as frequent and more complicated to be accessed than from Barcelona airport or Girona airport.
There is a direct bus service called Hispano Igualadina that connects Reus airport with Barcelona city, going to Sants Bus Station. Sants station can be accessed by underground with lines L3 and L5 and also by bus.
A single ticket from or to Barcelona costs around 13 euros, and the return ticket 22 euros and the journey takes approximately 1 hour and 30 minutes. To buy the tickets you need to go to the ticket office either at Sant station or in the same airport they have a box office too.