On foot
Every wood, slope or river, will have a marked trail beside or through it. Walking is very much a viable alternative to taking public transport, the Senda Sursilvana is a path that runs the lenght of the valley, passing through villages where you can stay.
By public transport
The Glacier Express (http://www.sbb.ch/en/inde...) the length of the valley, stopping at Disentis, as does the Rhatischer Bahn Graubunden's train service. Post Buses (http://www.post.ch/en/ind...) take you to the remotest of mountain villages and helpfully they are synchronised with the trains.
By car
The national route 19 runs the length of the valley. Roads run up the majority of the side valleys and all except remote villages are accessible via road. Driving in the area is very scenic and although a car may be slower than the train the car gives you the opportunity to stop at a cafe or take a fabulous picture.