The air ports in Costa Brava area are located in Girona and Barcelona The airport operator is Aena.  Information is available from their web site. Some tour operators use the air port Perpignan in France as well.
 

Transfer may already be arranged by your tour operator, else Taxi is not to expensive. Max persons in one Taxi is 4.
An alternative is to book transfer together with your hotel. This service is offered by www.alpharooms.com . An other possibility is www.resorthoppa.com  A2Btransfers.com
 

If you are planning to use public transport, the trick is to ask the tourist office at your destination. To find their address &Tel. or e/mail, use the official tourist web site for Spain: www.spain.info    Look in section for destinations, or use their search.
You can also look in section for "usefull web sites"   here, if a local web site is listed.
 

There is a train, starting in Barcelona, via Girona, Figueras, Port Bou to Perpignan. The train operator is  horarios.renfe.es/hir/ingles.html  Web is in english, and easy to use. Or look up time table in the French part the French train operator is needed.

www.fgc.net  Regional train service in Catalunya. Barcelona subway.

The biggest busoperator in the area has a web site with route plan and time tables. www.sagales.com

http://www2.alsa.es  A national and international bus operator. Web is in English as well.
 

Along the coast there are a lot of smaller boats sailing during the summer season. These can be used as transport from one town to another as well.