You can get in Avilés by plane the airport is near the city and well comunicated by bus and highway) The mail bus company, Alsa, comunicate the city whit all the provinces and the most important cities in the country. There're also dayly bus services every 30 minutes between Oviedo, Avilés and Gijón.
Yo can also get there by train. There are two companies, FEVE and RENFE. The first links the city with Gijón, the west of the province, the north coast os Spain and Galicia. The another one, RENFE, goes to Oviedo, the south of the province and the rest of the country.