Geneva Airport's own FAQ states that since 1 January 2022 the free bus/train ticket on the unireso network that used to be given to arriving passengers has been discontinued, yet most guides still send you to a machine in baggage reclaim. The free options that do exist are the Geneva Transport Card, which only accommodation providers issue to guests staying in a Geneva hotel, youth hostel or campsite, and the tpgAérobus, which only runs towards the airport.
The tpg timetables show tram 14 running Bernex, Vailly to Meyrin, Gravière and tram 18 running Grand-Lancy, Palettes to Meyrin, CERN. Neither serves the terminal. The airport is served by bus lines 5, 10, 23, 28, 50, 56, 57, 59, 66, 272 and 274 plus the train; you only meet tram 14 or 18 if you change at Vernier, Blandonnet or Meyrin.
Zone 10 is the whole canton of Geneva, which is why the airport is included, but it stops there. To go beyond it — Nyon, Lausanne or the French border communes — you need a Léman Pass ticket or a supplementary ticket on top of your zone 10 ticket, and the Léman Pass supplementary tickets are valid for 90 minutes.
Genève Aéroport states that only taxis authorised by the airport may pick up passengers, and the cantonal flat fares from the airport are CHF 25, 35, 50 and 60 depending on destination. Anyone soliciting inside the Arrivals hall or quoting CHF 100 or more for a city-centre run is selling a commercial transfer, not the regulated fare.
The cantonal regulation sets maximum tariffs of CHF 6.30 for a normal pickup and CHF 7.80 for a pickup inside the Geneva Airport perimeter, then CHF 3.20 per kilometre at tariff I (06:31–20:30 on weekdays, Saturdays until 18:00) and CHF 3.80 at tariff II (20:31–06:30, Saturdays from 18:00, Sundays, public holidays, or more than three passengers). The only legal extras are luggage: CHF 1.50 per bag from 5 to 30 kg, per pair of skis or per dog, and CHF 3.00 per bag over 30 kg. Waiting time is CHF 60.00 an hour.