Oviedo is both the beginning and the end of several caminos. Descriptions below are separated.
Arriving along Camino San Salvador: Shells and arrows will bring you right into the old quarters of Oviedo, passing a plaza and the beautiful Ayuntamiento building. There is talk of a new certificate which you can claim upon completion of the route, but details of where to find it are not yet sorted out. For now, you are advised to ask in the Cathedral or in the Albergue de Peregrinos.
Leaving along the Camino Primitivo: If you are starting your camino in Oviedo be sure to leave enough time to visit the Cathedral, which is the origin of the camino itself. It is also the place to pick up your credential (pilgrim passport) which will cost you 2.5€ but will include a visit to the Camara Santa. The road out of Oviedo is notoriously difficult. To make matters worse, there are too many shells on the ground to be helpful, especially in the center. They mark several of the caminos into town as well, and there is no distinction between the two. If you can get your hands on a city map, you are in good hands. This is how it is done: 1. With the main facade of the Cathedral to your back, walk to the opposite end of the plaza and take the exit on the right. This is the Calle San Francisco. 2. San Francisco ends when it meets Calle de Uría (350m from Cathedral). Turn right and follow Calle de Uría. For the first 250m, the Park of San Francisco will be on your left. Stay on this road, regardless of arrows or shells. It is about 700m long and ends at the train station. 3. At the train station, turn left along the Calle de la Independencia. Stay on the right-hand side of the road. You will pass 7 cubist looking buildings before the sidewalk turns sharply back to the right. Follow the turn and cross the road towards another cluster of 4 similar buildings with a plaza in front. From here it is safe to follow the arrows. 4. At the end of the plaza is a round about. Cross to the left (clockwise) twice and turn left along the Calle de la Argañosa. When it turns to the left (700m) you should turn towards the right, looking out for the pedestrian bridge which crosses the train tracks. 5. The arrows from here zig zag you through new development which ends quickly. By the time you get to an urban looking track and have left Oviedo behind, you will have covered about 3.6km provided you did not get lost. Oviedo fades from view quickly and with the exception of the capital of Lugo it is beautiful country walking the whole way. Buen camino!