Santiago de Compostela (SCQ) is the main gateway airport, with direct flights from Madrid, Barcelona, London, Amsterdam, and other European cities via Iberia, Ryanair, Vueling, and others. Vigo (VGO) airport also handles domestic flights and some European routes. A Coruña (LCG) has fewer international connections but is useful if you're heading to the northern coast.
By train, Renfe connects Galicia to Madrid (around 5 hours to Santiago on the high-speed Avant/Alvia), Barcelona (9+ hours), and within the region between the main cities. The train from Vigo to Porto in Portugal takes about 2.5 hours and is a scenic and useful cross-border option.
By road, the AP-9 motorway runs the length of Galicia's coast from Ferrol in the north to the Portuguese border at Tui. Driving from Madrid takes around 5–6 hours on the A-6.