The capital of Asturias is Oviedo. (200.000 inhabitants). The  main airport is situated 40 Km. from here. There are flights to other major cities in Spain as well as international flights. The airport operator is Aena. Information is available from their web site. (Look under Asturias).   Haven´t got the ticket yet. Click here for discount flights
 

From Santander there is a ferry connection to Plymouth in UK.  www.brittany-ferries.co.uk  This is a convenient route for Britt's going on vacation to Asturias, as well as other destinations in Spain.
 

Arriving by airplane, transport is needed. The most convenient way is to get a hire car. Keep in mind, however that when you get off the beaten track, the roads are narrow. A small car is handy is these situations.