For paraglider pilots, it’s completely unnecessary to bring a car, as the public transport facilities are so comprehensive. If you’re coming by air, you can fly to Zürich, Geneva, or even Milan and take the main line train to Brig, then change to the Matterhorn Gotthard Bahn narrow-gauge railway for the final leg to Fiesch. There are several campsites in the area, numerous apartments are scattered around the village, and there are plenty of hotels, some relatively inexpensive. Details can be found on the Tourist Office website. The popular impression that Switzerland is excessively pricey is true for fashionable resorts and big cities, especially with the strengthening of the Swiss franc, but in Fiesch you may find that you don’t pay much more than you would in other premier Alpine flying areas (e.g. Chamonix, the Dolomites) for the equivalent accommodation and food.
If you intend to stay in Switzerland for a while and to get around by rail, it may be worth investigating whether you could benefit from a Swiss Half Fare card. This entitles the holder to a 50% discount not only on the trains and post buses, but also on many uphill transport facilities (including the Fiesch gondola), for which you can also buy a chip card for 6 or 12 trips at a much lower rate than for single journeys.
The Fiescheralp takeoffs are served by a 10-person gondola which runs continuously throughout the day. It only opened in late 2019, so I have yet to use it. Last summer, I was told that there would be arrangements to take hang gliders, but I have as yet no idea if this is correct, and I expect that there will be an extra charge for this facility. I will update this page once I have definite information.
Trains run along the valley floor in both directions every hour. You are allowed to pay for your ticket on the train only if you get on at one of the smaller stations which have no ticket office or machine; otherwise, you must buy it at the station before boarding. Be aware that the last train from Chur along the valley floor towards Fiesch which enables to you to get back the same day departs at 16.56! However, if you have missed that connection, your latest option departs at 19.09, goes via Zürich and Brig, and arrives at 23.23. Hitchhiking back along the valley floor, which in my experience is easiest in the peak tourist season, can be quicker than the train if you are lucky.