How did "small businesses" (or the equivalent) work in the USSR?

Soviet economic arrangements are bit out of my area of expertise, and I was hoping someone could enlighten me over something I’ve been puzzling about—or at least give me some pointers on where to start reading.

That is, how did “small businesses”—or at least what would be a small business, in the west—work in the Soviet Union? I mean, things like a barber shop, or a bar, or—I dunno, a tailor or a coffee shop. Things that don’t strike me immediately as being in the same league as a state-owned store or factory.

Was everything where money changed hands a government-owned business or franchise, or else simply non-existent, or something? I honestly have no idea. But I’d be fascinated to find out more.

And of course, I realize that this is concerning a large country over almost 75 years of political and economic changes, so the answers might vary wildly—and even more considering the differences in what might have been “official” policy and what actually happened in practice.

So…can anyone help me out, according to my need?

You have answered your own question, it varied widely according to time as well as region.

Contrary to belief, the Soviets never completely abolished private businesses ever, and after about 1970 gave up on trying to.

Have you tried Googling? Searches for “private enterprise in the ussr” turn up a lot of scholarly articles on the subject. One of them, “The private sector in the Soviet Union and China” from a 1989 issue of Intereconomics, describes some contemporary reforms and gives statistics on private enterprise in the late 1980s. For example, it says that less than 1% of the work force was employed in private enterprises (“voluntary cooperatives” and “individual enterprises”). It gives a breakdown of the sectors for the 48,500 voluntary cooperatives (but not the 300,000 individual enterprises), and summarizes the basic rules for these private-sector cooperatives and sole proprietorships.

I’ve just noticed that the article I mentioned is behind a paywall. In case you can’t access it yourself here are a few short quotes from it which I think address some of your questions about small sole proprietorships:

The article also discusses private cooperatives, which at the time enjoyed much less regulation and restriction. They were free to operate in pretty much any economic sector, had no limits on the number of employees, and could even conduct foreign trade. Still, their activities were dwarfed by the public sector.