The bus is a city bus that you can catch in calle Uria. It's the 1A, with Centro Asturiano as its destination. Centro Asturiano is what some guidebooks refer as a sports center. There is a bus per hour. You can also walk up, but it's a brutal walk.
http://www.tua.es/es/lineas-y-horarios/linea-a.html#paradasIda
http://www.tua.es/es/lineas-y-horarios/linea-a.html#paradasIda
When you are done visiting, head back to the bus stop/parking lot and walk in the same direction the bus was going, to the right when you have your back to the monuments. And just keep going. You will pass a small village, Uccle, with a bar, then when the road ends, take a left on the perpendicular road. Keep walking until you come to a small white chapel on your right. There is a stamp there. That is where the Naracanco routes joins the normal route out of Oviedo.
At the chapel, get off the road, hop on the grass and take the path marked with your first yellow arrow.
Naranco to Esclampero may be 10km or so, so a nice short day for the first day of walking, helping get over jetlag.