Chenini is 18 kilometres west of Tataouine, and virtually everyone arrives from there. The road is paved and in decent condition.
The simplest option is a taxi from Tataouine — a return trip with waiting time at the village can be negotiated for a fixed fare, typically around 20–30 Tunisian dinars depending on how long you want to linger. Agree the full price before you leave.
Shared louages (minivans) run from Tataouine's louage station, though they are irregular and more useful for getting there than for getting back, since the last vehicle often leaves Chenini early in the afternoon. If you take a louage in, plan to either walk back to Tataouine or arrange a taxi from the village — options are limited once the day-tripper traffic thins out.
There is no direct public transport from Tunis, Sfax, or Jerba to Chenini. Fly or take a bus to Tataouine and connect from there.