From most places you have to fly through Madrid on your way to/from A Coruña. In A Coruña, there is a bus going from downtown to the airport, you can also take taxi, it takes approximately fifteen minutes. The harbor is in the city center, close to the Old Town.
You can also take the train to Santiago de Compostela. The train takes less than an hour. Ryanair, among others, are flying from Santiago.
La Coruna Airport: http://www.aena.es/csee/Satellite/Aeropuerto-A-Coruna/es
Santiago Airport: http://www.aena.es/csee/Satellite/Aeropuerto-Santiago/en/Santiago.html