The main takeoffs are at Fiescheralp, and are reached by an efficient 10-person gondola starting from the train station, which is around five minutes walk from the Fiesch landing field. It runs continuously throughout the day, with specially adapted facilities to take hang gliders. Riederalp is a reasonable alternative but it is lower and less easy to reach from the village.
Talegga and Salzgäb are unofficial hike-and-fly options.
There are also takeoffs above Bellwald, which I have never used.