Here are the routes that we would drive coming from the airport to Arinsal, as well as links to Google maps with the routes marked on.
From either terminal when you come out of the airport follow the blue signs for A2 Lleida. After a few kilometres the motorway splits between the AP2 and the A2 - keep following A2 as you have to pay to use the other.
Once on the A2 you'll go past a couple of signs for Andorra but just ignore them as you want to come off at exit 520 signed Ponts and Andorra. At the roundabout take the second exit onto the L311 towards Guissona, and then the L313 to Ponts - Andorra has recently been added to lots of the signs from here, however you want to head for Ponts. In the centre of Ponts turn right onto the C14 and head for La Seu d'Urgell.
Once at La Seu you'll bear left to a roundabout and then you're only 8km from the Andorran border. From the border follow Andorra la Vella, and as you come into the city there's a left turn at a mini-roundabout for Ordino - keep following this until you come in to La Massana, and at the end of La Massana you'll see Arinsal signed.