Lets start off with the most basic need of all, water. This is the hardest one to come by if you are a nomad. Water sources are valuable, and typically guarded, be it by monsters or by villagers. There are a number of ways one might get moisture from the environment, however. Nomads are typically herders, so the tribe likely keeps kanks or some lizardlike similar creature as mouts, beasts of burden, and sources of food and materials. Kanks make nectar, which although apparently foul to the taste, must have a significant liquid content. There are also plant sources of water, which usually come with some food value in the bargin. Cactus meat is the most obvious, but there are likely tubers and roots that can be gathered for both food and water content. The blood of livestock might be a moisture source as well, either as a emergency measure, or perhaps even as a staple, depending on the culture. All of these means are likely to greatly stretch the water in the tribe's water skins quite a way.
Even still, the tribe will from time to time need to water their stock and refill their fresh water supplies. Within their home range nomads might perhaps have hidden wells they can draw on, and would certainly knew all the natural water sources such as any springs. Eventually, the tribe will likely have to obtain water from a "claimed" water source, one under the control of a village, trading post, caravansari, etc. This means trade. It is unlikely that nomads have much in the way of coin, although they likely have some, but they likely have crafts and gathered materials they can trade at the village for some time at the well. Here I am thinking things like fiber crafts, cordage, baskets, medicinal plants and herbs, surplus nectar, bone, horn, hide, shell, etc, both from their flocks and what they hunt. Perhaps if they come across a supply of semi-precious stones like aggates or a good piece of flint this would be good for trade. Beyond the price of thier water needs, any surplus would purchase what few manufactured goods they do not make themselves. Metal goods are likely well beyond their price range, but from time to time nice quality textiles, glass or pottery, etc, are likely picked up at the trading post.
Assuming the tribe can keep everyone in water, food would likely be less of an issue. Again, their herds would supply meat, nectar, and blood. They would also likely hunt, trap, and gather, putting a huge range of reptiles, insects, small mammals, roots, seeds, tubers, and other plants on the menu. As long as they could stay where the water was they would likely stay fed.
The next big issue is defence. There are plenty of folks in Athas that are wiling to rob, enslave, and eat you. Pretty much everyone in these tribes would be considered a warrior. The best defense if still likely staying alert and keeping the heck away from those you don't know well, but just about everyone would likely be trained with some kind of ranged weapon (sling, javelin, bow) and the more physically capable would be weilding spears, clubs, shields, etc. They aren't going to face down the legions of Urik by any means, but the can likely break camp in minutes and unleash one heck of a ranged volley from the back of their kanks.
A tricky question is how large of a group would be optimal. If you are too small you are easy pickings for enemies. If you are too large you need too many resources, and strip an area out too fast. If you eat all the cactus and rats and bugs etc there aren't any here the next time you come through. For this one I am open to suggestions.
Anyway, this is mostly thinking out loud. I am not sure how any of this comes up in actually play, but this is the sort of thing that goes through my mind when I am thinking about a campaign. If anyone has any thoughts throw them out there.
The Athasian counterpart is probably tougher in a fantasy sense, but it is a relatively new development on Earth that in general, nothing is trying to enslave, rob or eat you. Most of them and environment certainly depending.
Don't forget to look over the Pueblo peoples and Navaho tribes from the desert Southwest. Arizona is Athas' version of the Garden of Eden.
As a rule of thumb, a group of 30-50 people plus animals seems to be optimum for Earth nomads. Smaller (family-only) groups and large (100 people) will be a temporary thing during hard times or when near a known danger or trying to make a long move.
The nomads will make Artwork for trade with settled people; nomads need high-value, low-bulk, lightweight articles because they literally have to carry everything they own with them. Spices or sweets or drugs (both kinds) would work too. So would enchanted fruits/nuts, if the nomads have a druid available. Or perhaps one member of the tribe is a Masterwork craftsman.
I don't know if it is still on the web, but 10 years ago I contributed some relevant material to the Tamerthya website. Look in the Gamma World section for the page on the Zona Nomads.