When I think of common people owning land for themselves, I think of the idea of the yeoman farmer in the United States, but even then I am quite ignorant on that.
This is one of those questions that is lost in the mists of time. As far back as we know, people owned land. We have letters from 4000 years ago from a landholder and minor priest, Hekanankhte, who wrote to his agent with instructions on the handling of his land, specifically referring to "his land" on three separate occasions. There is other evidence from Ancient Egypt the mid-third millennium of transfers of land by private people.
We don't know how representative Hekanankhte was, though he did resort to cutting his family's food allowances during a year of crop failure (and said that he had cut his own even further), so he wasn't exceptionally rich, on the other hand he does refer to various servants, and he was either literate or could hire a scribe, so clearly he wasn't that poor either. Sadly this is true of the vast amount of economic history, we lack distributions. But, I have never heard of a land reform granting the right to buy land to commoners specifically (as opposed to general opening up in post-communist states).
Please note that I am in no way a reader of ancient Egyptian hieroglyphs and am entirely reliant on secondary sources here.
Sources
Ezzamel, Mahmoud. 2002. Accounting for Private Estates and the Household in the Twentieth-Century BC Middle Kingdom, Ancient Egypt. Abacus 38 (2): 235. doi:10.1111/1467-6281.00107.