Getting to and from your starting point on the Camino de Santiago can be an adventure in itself. There are many great tool out there to help.
A great all around travel site for Europe is rome2rio This is a travel planning site that I use to find the best way to get from one point to another in Spain, although it is great for most of Europe.
Ryan Air is a quick and inexpensive way to get from Santiago to Madrid. Iberia also flys from Santiago to Madrid but is a bit more pricy. Others that fly out of Madrid are Vueling and Air lingus.
For Train Travel:
For Bus Travel:
Alsa I used Alsa to travel from Santiago to Lisbon. They travel much of the country.
Avanza Bus I will be using avanza to travel from Salamanca to Madrid Barajas airport in May and then will use them again when I return to complete the Via de la Plata.
For travel from Biarritz to Saint John Pied du Port:
Caroline Aphessetche @ Express Bourricot is fantastic. (+33) (0)6 61 96 04 76
Please leave me a comment with any others that should be added to the list.