Obviously, there are no written records of prehistoric times. Whatever we know comes from archaeological excavations, but archaeology has its own bias in that big things outlast little things. The artifacts left by large groups are easier to find than an isolated hearth or small camp occupied by just one family. So if you find half a dozen large settlements but no smaller ones doesn't mean smaller ones didn't exist.
There are a couple of ways in which researchers approach such questions. One is through mathematical modeling of resources. Hunter gatherers need to eat, and food resources have a certain density and distribution, depending on environment. With appropriate data, you can figure out certain things, such as upper limits on the population a given ecosystem can support, given different levels of competition. Or the most efficient way to use the resources, to draw a reasonable balance between calories acquired from hunting/foraging and calories spent in doing so.
From such studies, we can draw a few conclusions. First, there was no norm that was constant through time and geography. It very much depended on local environment at the time. Grasslands won't support the same population density as forests or deserts or coasts. The availability of resources and their proximity sets upper limits on group size. Resource poor environments support smaller groups than resource rich environments.
The type of resources also matter. The percentage of calories from animal and vegetable sources varies, and so do the strategic requirements for obtaining them. What is the primary source of calories? Is it big game? Is it roots and tubers? Is it small animals caught via traps? Is it fish or other seafood? All of these exert different dynamics on group size.
There are some generalizations you can make. Larger group size is favored because it's more efficient for food gathering, and because it spreads out risks more evenly. However, it can also lead to conflicts or other social problems, and it can't exceed limits set by resource density.
Based on these considerations, many anthropologists believe that ancient hunter-gatherer societies were tiered. At the low level, there was the family group, which consisted of 4-6 individuals, the nuclear family. They probably hunted/foraged alone most of the time. There were other family groups using the same territory who probably cooperated with each other in hunting/foraging, and the family groups aggregated and dispersed periodically during the yearly mobility cycle. Occasionally, there were much larger aggregations, once a year or perhaps once every few years, which may have served socioeconomic purposes such as trade, exchange of members, etc.
Another way of studying the subject is by examining hunter-gatherer populations that survived to modern times. One study I know of is based on Binford's aggregated dataset of 339 hunter-gatherer societies, which was based a huge range of published ethnographies.
Marcus Hamilton did a study on group size in this dataset. Here's a figure from his paper showing group size at various levels in the hierarchy.
Note that the y-axis is logarithmic. The x-axis show the Horton order, which is basically a measure of branching complexity, since the paper was about their branching hypothesis. What's important here is that the numbers represent different group hierarchies:
Again, these are averages of 339 different hunter gatherer societies from all over the world, coming from a mix of climates and ecosystems. The gray boxes for each level of the hierarchy represent the 95% spread, meaning 95% of observations fall within them. The circles above and below are outliers.
As you can see, the average size for the family group is 4-6 people, usually consisting of father, mother and children. This group hunts/forages alone for some of the time, and together with the extended family group for some of the time.
The extended family group consists of people closely related by blood to the family group - cousins, uncles, aunts. The average size of the extended family group varies over the course of the year. During the "most dispersed phase", it averages about 10-14 people. During the least dispersed phase it could grow to 50-90 people.
Although individual experiences would vary significantly by which hunter-gatherer population we're talking about and what resources they seek, you can imagine a "typical" scenario this way. For part of the day, family groups would be foraging together. They would either be in sight of one another, or at least aware of where the others were even if they dropped out of sight occasionally. For part of the day, or perhaps once every couple days, the extended family group would work together. This could mean that 2-3 adult males (out of a group of say 14) might go hunting together. Or the women might be working together, either gathering food or making clothing or whatever else they needed.
This would be the routine for much of the year. But for part of the year, the group size would increase, perhaps to 50 or even 100 people. This might happen, for example, if there was a resource that became seasonally available (a migrating herd of animals, certain fish spawning or becoming abundant seasonally, whatever). How long such larger groups last is very variable, it could be a few weeks or a few months.
Once in a while, every 2-3 years or so, there are larger gatherings. These are usually deliberate movements of people not enforced by chasing the food supply but rather for socioeconomic reasons - trade, marriages, etc. They can be anywhere from 100-300 people, or even more depending on the population.
Some references:
Hamilton, M. J., Milne, B. T., Walker, R. S., Burger, O., & Brown, J. H. (2007). The complex structure of hunter-gatherer social networks. Proceedings. Biological Sciences / The Royal Society, 274(1622), 2195–2202.
Binford, L. R. (2001) Constructing frames of reference: an analytical method for archaeological theory building using ethnographic and environmental data sets. Berkeley, CA: University of California Press.
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