Caesar has stated that he has "We have cities of our own, but nothing compared to Vegas..." to me this would mean they have civilized people doing "average Joe" stuff like farming, building and shopkeeping. Crime is nonexistent in their lands because of how well they enforce law there, so maybe there is a tough presence of military guards stationed every few blocks - possible Frumentarii amoung the people reporting any suspicious behaviour to said guards.
I'd say the men who are born into the Legion but aren't fit enough to be soldiers and not too unfit to be killed are given work on building the homelands along with the women.
The people we see in the Fort, I take to be recently enslaved women who are part of NCR or unknown tribes, those born into the Legion are given their place back home but can never serve in the Army.
The Legion have their own currency, coins, so they should have some structure in earning and spending those coins: Earning would be through work on the farms, construction and scavenging useful materials/weapons, and obviously spending it on food/drink and other misc things needed to live, also trading with any caravans who deal with Legion.
It's all assumption until a Dev or someone says otherwise.
Perhaps this is a bit off-topic, but what always baffled me about the Legion's design as a faction is the oft-stated remark that "the Legion's lands are completely safe", as if being a police state automatically equals no crime. In fact, often times it results in the exact opposite from occuring. The Soviet Union was one of the most highly policed countries in the world in its time, and smuggling and crime still flourished, with local Party officials often taking a cut in the profits. This is also true in China, where corruption amongst low-level Party officials runs rampant, as they often use their position to secure favors for businesses run by family members, and even evict people from their land. In real life, putting a soldier on every inch of territory does not result in security, but apparently in the Fallout world, it does. If this logic held, East Germany, which had one Stasi agent, informer, or part-time informer out of every six of their citizens, would still be around, and be the most crime-free place on earth.