A zeer pot is quite simple. It's basically two large earthen pots, one nested in the other. The space is filled with sand and water is added. A damp cloth covers the top. As the water evaporates, the inner pot containing the perishables is kept cool in the same manner that a mechanical refrigerator operates -- water evaporation draws heat from the inner vessel. Water is added twice a day.
Muhammed Bah Abba is credited with reviving (some say inventing) use of the zeer and has his own instructions on theory, application and making one. I am going to make one of these myself and see how long basic vegetables will keep at room temp. You can see from the picture how easy it would be to improvise a zeer with regular flower pots. I will then give it a taste test after one week.