In mediaeval times a pilgrim started literally from his front door – he would have had his mass before setting off where his staff and cloak would have been blessed and would have been issued with his testimonicales from his overlord giving him permission to make the journey (indeed after 1388 it was an arrestable offence to travel without this document which gave access to the privileges of a pilgrim and hospitality). He would have set off on foot (or by horse or donkey if he were richer) and, from Britain at least, set off to one of the ports before catching a boat, undertaking a sometimes dangerous sea crossing and then walking further to Santiago.
A blog about the Pilgrimage to Santiago de Compostela