Basically it would have to work the way real nomadic empires work: you gain yields by pillaging them from settled civilizations.
It would be an interesting playstyle because it would not only encourage but require you to be in a constant state of war, and as such should probably feature a special ability wherein warmonger penalties are treated as though you were one age earlier, you get a significant bonus to all pillage yields, but any city you conquer and keep takes a severe penalty to all yields and is considered occupied for the duration of the game (not just until the city is ceded in a treaty).
Not entirely. Nomad/Pastoral Cultures could access a wide range of resources without 'pillaging' them from outsiders: herd or prey animals (primarily cattle for the Asiatic, Bison for the North American) which gave them leather, bone, glue - almost all the makings of the saddlery and composite bows that made them so deadly. They could also trade in 'third-party goods'. That is, being nomads they were in contact with many different peoples, and traded goods obtained from them by raid, extortion or trade to other 'settled' neighbors. Many 'Nomad' groups were classic 'middlemen' in Trade - the Khazars, Tatars, Xingnu all dominated or controlled parts of the central Asian 'Silk Road' at various times, for instance.
The way to make a Nomad 'Civilization' viable in the game, I think, is to give them two basic and unique abilities:
1. From the start, they can establish Trade Routes that originate in other Civ's cities or City States. In other words, the origin 'city' of the Trade Route is actually the Nomad Camp, and it is the 'Trading Post' if you will, Between the two destination cities. The destination cities would get some benefits, depending on what is being traded (as the trade benefits vary now between cities) while the nomads would also get possible Gold, Religion, Production, or even Culture benefits.
2. Rather obviously, the Nomad 'cities' are actually Camps and can move. Therefore, they cannot have Buildings, but each camp would automatically control a larger territory than a settled city, and each nomad military unit would come with one 'Builder Charge' which could be used to build a Pasture or Camp to extract resources within the territory. Keeping in the spirit, Nomads cannot build Mines or Plantations, but any Builders they capture can build them for them, (and it might be advisable to give them the Aztec Eagle Knight ability to convert defeated enemy units into Builders) and they can get the benefits of any resources so obtained. Nomad camps/cities can have Districts, also mobile, as smaller camps. I suggest that the only nomad 'district camps' would be the equivalent of Holy Site, Encampment, Campus, and Commercial Hub. Their versions would have to provide some of the capabilities of the Buildings usually associated with the districts, but more limited: no equivalent of a University, for instance. But equivalents to Shrines or Temples, Markets or Libraries are feasible, under different titles: Sweat Lodge, Shaman Hut, Trade Meet, Sacred Mountain/Grove/Lake/Hot Spring, etc.
Eventually, to be competitive, the nomads will have to settle down and either found or capture a 'real' city. But historically, major nomadic/pastoral civilizations had enormous influence right up to the start of the Renaissance, or for about 150 - 200 turns of a Civ game. The time frame alone is reason enough to include a mechanism to represent them in the game.