There are three airports in Spain near Braga in Vigo, Santiago, and A Coruña.
Vigo (VGO) is 100km away from Braga by motorway.
Santiago (SCQ) is 200km away from Braga by motorway, there are frequent trains and buses to Vigo.
A Coruña (LCG) is 250km away from Braga by motorway, there are also frequent trains and buses to Vigo.
Avis, Europcar and National Atesa have offices in the three airports.
Iberia and RyanAir fly from London (Heathrow and Stansted) to Santiago .
Air France flies from Paris to Vigo (expensive, >300 euros).
Iberia and Spanair fly from Madrid and Barcelona to Vigo, Santiago and A Coruña.
Air Europa flies from Madrid and Barcelona to Santiago de Compostela.
Usually Spanair and Air Europa have the cheapes prices. Actually Spanair has started recently to fly to A Coruña from Barcelona and Madrid, and to Santiago from Barcelona and is offering very cheap tickets on those routes (from 90 euros return).
Information about Spanish airports is available from AENA.
Train information is available from RENFE.
La Coruna information including bus timetables http://www.aytolacoruna.es/en/index.htm.
Bus timetables for main Galician lines http://www.todocompostela.com/autobuses.asp (in Spanish).