There are two choices:
1. Use the Spanish postal service, Correos. You can now arrange everything online instead of telephoning them - see the link below:
http://www.elcaminoconcorreos.com/en/rucksack-transfer
note that a rucksack transfer also includes a suitcase.
You can do everything in advance for the whole journey - € 20 Euros, or book each transfer for € 5.
The luggage cannot exceed 20kg.
There is one major wrinkle in that if you stay in a municipal hostel, Correos does not transport there, and so you may need to pick the luggage up at the local branch of Correos, which may not be nearby (e.g. Hospital de Bruma). You either need to be staying at a private hostel or hotel.
But, the transfers are efficient (you need to have everything ready by 9am and they deliver by 5pm) and like magic, when you arrive, you bag is there when you arrive.
2. Arrange a trip with a tour company, where that tour company will transfer your luggage. The tour company will book the hotel (sometimes with meals provided), arrange a credencial and transfer luggage.
Examples of such companies are Follow the Camino, Camino Ways, Macs Adventures and Tee Travel (who are actually the local, on the ground company that foreign companies cooperate with). Using a company like this is more expensive, but it means everything is arranged for by someone else. You are though fixed for a schedule that binds you, although the Ingles is only a 5 or 6 day walk