The main way to get to Corunna is by plane. Two options are available.
Option 1: Local airport.
A Coruña airport (LCG)
(a.k.a. Alvedro) is the recommended option, since
it is just 8km away from Corunna downtown. Most flights will connect
through Madrid or Barcelona. There may exist direct connections to other
European capitals like London (Heathrow), Paris or Lisbon, but they
usually have a limited frequency and may vary along time. Check updated
information at the Alvedro destinations
webpage maintained by AENA (the
Spanish Civil Airports Network).
There exists a bus connection to the city (every 30 minutes on work days
and every 60 minutes on the weekend), but taxis are cheap and more comfortable.
Option 2: Santiago de Compostela airport.
A second option you may consider is
Santiago de Compostela airport (SCQ)
(a.k.a. Lavacolla) which, despite of being 65km away, it allows more flight
combinations. Check the updated list of destinations
maintained by AENA.
For connection from Lavacolla to Corunna, the simplest method is a taxi (it
may cost around 50-60 euros and take 45 minutes) and, of course, could be a
good solution if you travel in a group. Otherwise, you can pick a bus to
Santiago train station (25 minutes) and then a train to Corunna (30 minutes).
The total cost can be around 10 euros and the total time may vary depending
on the bus