It really could function in a myriad ways. The first thing I envision would be something like the medieval European village society, but without private ownership of shares of the fields. I think I read about something broadly similar in Russia, with regular redistributrion of plots according to the number of adult men in a family. A system like that could work. You would, of course, have village communities that were relatively self-sufficient, with producers of the few needed outside items organised differently. Perhaps you would have village-based craftsmen (cities are not required for even relatively sophisticated premodern societies, though they make things easier). Alternatively, you could have a system where you could choose to move into the city and become part of a different society owning different means of production. The cities would need to come by a population somehow, and they aren't going to be self-sustaining.
What you couldn't have was central planning. That's a feature of most modern Communist regimes, but it owes more to its enormous popularity around the first half of the twentieth century than any inherent collectivist virtue. But you could easily see a society where autonomous, self-organising groups of producers - guilds, villages, miner knappschaften, fishing flotillas - own the means of production and produce a surpolus for trade with other such communities. Of course, for a society to maintain that status quo,, you will either need to posit a strong central authority with a vested interest in it - religious, perhaps - or a strong taboo against individual ownership of means of production. There is also no need to assume such a society would be egalitarian, democratic, enlightened, or nice.