Public transportation around the chott is not the best idea, as it will involve some waiting, and you will be forced to pass many interesting places.
The best is to rent a taxi for the day in Kebili or Tozeur.
Both of these places have car rentals with about the same prices as anywhere else in Tunisia.
You can also go with your travelagency as we did.
It can get extremely hot out here, so take all necessary precautions
The best way to get across the Chott el Jerid is on the causeway. Before this was built (fairly recently) there was only a dirt track and journeys across the lake used to take much longer.
When driving trough the Chott, a jeep will come in handy. You'll notice the tracks of other persons that left the road to take a ride in the sand/salt.
Travel agencies will offer trips to visit the Chott El Jerid. We traveled with TTS (located in Jerba) and where very pleased by the service and the trip.