From Barcelona Airport

By Taxi - this is the easiest way to get from the airport to central areas, the cost of the run is about 25 Euros. All official Barcelona taxis are black and yellow and are meter operated (Plus any surcharge. Surcharges include a supplement for travelling from the Airport, or to or from the port and also for each suitcase, all surcharge rates are displayed in the back of the taxi).

Aerobus Barcelona - The aerobus service is a shuttle bus service that links Barcelona airport to the city centre. This service normally runs every 15 mins and stops at all 3 terminals. Tickets can be purchased on the bus.

Trains - Overland rail connects the airport with Barcelona Sants Station, then use the underground system to complete your journey. Trains also stop at the secondary station of  Estacio de Franca, however this station is not serviced by a metro stop.  The metro runs directly from Barcelona Sants station and from Passeig de Gracia.
Barcelona Sants station is a major rail station that offers train connections to many other destinations outside Barcelona.
The train will drop you off about 5 mins walk from the airport main entrance. Much of your walk will be via a conveyor-assisted walkway which makes it quick and easy if you have luggage to carry.

Car Hire - There are 4 companies that offer cheap car hire from the airport.

From Girona Airport

Girona Airport is 103km (64.2 miles) North East of Barcelona or about 1hr 20 mins train ride from Barcelona centre.
The Barcelona bus is the most convenient method of transfer between Girona Airport Barcelona and Barcelona city centre. The bus service is run by an independent company and has no direct business association with Ryan Air. However Barcelona Bus arranged its times of departure and arrival to co-incide with the arrival and departure of RyanAir flights.
The bus stops right outside the airport and will take you to Estacio d' Autobusos Barcelona Nord (Barcelona's main bus terminal) in Barcelona city centre. From there you can continue your journey by  underground. The nearest Metro stop to the bus station is Arc De Triomf (Red Line, L1).
The Journey time from Girona to Barcelona city centre is approximately 1 hour 10 mins.
Also be aware that there are 2 different Barcelona Buses which are both operated by the same company. One bus leaves Girona Airport and goes directly to Barcelona (and vice versa) the other bus only leaves from Girona centre and goes to Barcelona (and vice versa) make sure you're catching the right Barcelona Bus.

By Taxi - The journey from Girona Airport to Barcelona City Centre by taxi is an expensive option and will cost you around 120 Euros for a single trip. A better alternative may be to stay in Girona overnight and use public transport the next day.

Around Barcelona

By Underground - Barcelona underground system is clean, efficient and air-conditioned. The 5 lines are easy to use and link all major sites.

By Bus - Barcelona has an efficient bus network covering the whole city.

By Taxi - Taxis are meter operated and easily available. They are an inexpensive alternative to public transport.