In hunter/gatherer days within small bands, and also to a large extent within families (but perhaps a bit less now) the method was Generalized Reciprocity[1], where people basically take care of each other and share. This was supported by the extremely fertile and bountiful forests and other resources that were shared between early people.
Later, the large "water monopoly" cultures like ancient Egypt had largely Redistributive economies, where resources flowed to the center (the Pharaoh, etc.) and were distributed again outwards.
Finally we got Market Exchange, where people bargain in the marketplace for goods, and this has been efficiently able (to a greater or lesser degree) to distribute resources for hundreds of years. Of course we have some redistributive elements like Social Security and Welfare, but these are limited.
Market Exchange relies now on basically everyone having a Job or another means to acquire money. But with automation this breaks down because jobs will more and more be taken by the AIs and then by robotic AIs.
So only a few possibilities are likely: either we end up with almost everyone a pauper and increase dole payments just up to the point where there's no revolution, or we somehow end up with everyone owning the AI resources and their output, taking the place the forests and other ancient resources played in hunter-gatherer days, and everyone can eventually be wealthy.
It looks as if, at least in the USA we are going down the path of having a tiny oligarch class with everyone else locked out of ownership of the products of the AI, but this may not be true everywhere, and perhaps somehow won't end up being true here.
[1] Stone Age Economics by Marshall Sahlins https://archive.org/details/stoneageeconomic0000sahl/page/n5...