There are various methods of getting around the city and the country here. I'll provide a glimpse into how I get around, both on a daily basis within the city, and less frequently on my travels further afield.
The most popular mode of transportation in Asturias would be walking. There are also buses that bring you around the city and Alsa buses that bring you to different cities. There are trains between cities in Asturias and the rest of Spain, and of course cars to get around.
Oviedo, especially the part of the city I live in, is hilly. When I first arrived to Spain, I lived in a city called Gijon that was completely flat. Walking was a breeze! When I moved here, I quickly found out how different things were. Hills, hills and more hills. The city is so hilly that there are escalators and elevators scattered throughout the city at some of the steepest points. Although it is tiring, the city would not be what it is without it. The spectacular views and viewpoints make it well worth it. I have also taken advantage of the hills to try and get in shape, and I can see a difference. The only other detractor to this option is the rain! It rains often. Most of the time it is a light sprinkle, but you need to make sure to carry an umbrella.
