Virtually every airline flies into Madrid, including Ryanair, easyjet, and Iberia from Ireland and the UK, as well as most US airlines.
Coming from the airport in Madrid, you can catch a shuttle bus to the main train station in the city. From there, you can get a train straight to Ponferrada. This journey will take 4 hours.
Ryanair, Aer Lingus and Iberia/BA fly direct to Santiago de Compostela from the UK and Ireland. Ryanair flies from Stansted, Iberia/BA operates from Gatwick and Aer Lingus operates from Dublin. Santiago de Compostela can also be reached by a number of locations around Spain and Portugal, as well as major European cities. Iberia/BA offers the best selection of flights and you can fly to and from Santiago De Compostela returning to Frankfurt, Paris, Rome, Barcelona, Bilbao, Fuerteventura, Gran Canaria, Lanzarote, Madrid, Malaga, Palma, Seville, Tenerife and Valencia.
If you are coming from Santiago Airport, you can take the train or the bus. For the train, head into Santiago de Compostela and then catch a direct line to Ponferrada (this will take 3 hours and 30 minutes). For the bus, head for Santiago city centre, and then catch a bus to Lugo, changing once in the bus station before heading to Ponferrada.