The traditional way of getting to Santiago de Compostela is by walking about 780 km from St. Jean Pied-de-Port in France, on the Way of St. James. It is just as traditional to arrive on horseback, though considerably more difficult in terms of facilities. You may be able to stable your horse with a local farmer, but virtually no hostels provide this service. Cycling is also popular.
Other way of getting to Santiago is by bus. The bus station is located in the outskirts of the city, but there you can get a public bus or a taxi to get to the city centre. You can get to Santiago by bus from several places:
From cities and towns of Galicia, try Arriva or Monbus. Unfortunately, the last link is only available in Spanish.
From other parts of Spain, try Alsa, one of the most important bus companies of Spain.
If you want to arrive to Santiago by train, you should visit the RENFE. The train station is relatively close to the city centre.
By air, the closest airport is Lavacolla (ICAO: LEST, IATA: SCQ), about twenty minutes by bus from the city centre. The following companies operate currently at this airport:
Adria Airways: Ljubljana
Aer Lingus: Dublin
Air Berlin: Palma de Mallorca
Air Europa: Fuerteventura, Lanzarote, Gran Canaria, Tenerife and Caracas
EasyJet: Geneve and Basel
Iberia: Madrid and Bilbao
Ryanair: Frankfurt, Milan, London, Madrid, Barcelona, Valencia, Alicante, Malaga, Palma de Mallorca,Lanzarote, Las Palmas de Gran Canaria and Tenerife
Volotea: Venice, Ibiza and Menorca
Vueling: Barcelona, Málaga, Paris and Zurich
Turkish