Early on, we'd have trouble with large predators, but history has shown enough times our willingness and ability to go toe-to-toe with much larger animals and wipe them out of an area if they pose a danger to us. Between fire, traps, and weapons, if we're capable of taking out whole herds of mammoths at our current size for food we'd be just as capable of killing proportionally mammoth-sized wolves and the like for our own protection.
Domestication could be interesting. The animals that are easiest to domesticate are herding herbivores. Cavies, hamsters, and similar rodents live in groups and could replace our sheep as a grass-eating source of meat and milk, but while sheep are migratory, rodents often live in burrows. This might lead to earlier farming and fewer nomadic human groups. Some of the larger burrows might even become repurposed for human habitation. On the other hand, we might just go and domesticate sheep and cattle anyway. We managed to domesticate elephants, after all. Dogs could be trickier - wolves would be too prone to viewing us as snacks, so we'd probably kill them rather than ally with them. Some crazy person might manage to tame them at some point, but they probably wouldn't be man's best friend in the stone age.
One interesting possibility that might greatly change things is the ability to domesticate and ride large birds. If we could pull this off, travel would become very different, very early.
Beyond our relationship with animals, life probably wouldn't be much different. Natural non-biological landscape obstacles tend to be distributed on a logarithmic scale, so while the tallest mountains would seem taller and the widest oceans would seem wider the structures we dealt with on a daily basis and the distances between them would feel about the same. This means that the wheel would be just as useful; our roads would be narrower but we'd have to clear out the same amount of material proportionally to make them. The square/cube law might make us able to travel proportionally farther in a day on foot so cities might still be spaced out about the same as ours are, but by the same measure it would be easier to clear the roads by hand so the pressures would balance out.
We're already way out of our league when crossing seas, so we'd probably manage to do it in about the same time period. We might start out with proportionally larger boats, which would mean larger groups of people settling in new regions, but not to the extent that life would be significantly changed.
The more we advanced technologically and shaped the natural world to our own whims, the more things would start to resemble our own world. Most high technologies would either work just as well on small scales or we'd compensate for physical limitations by making them proportionally larger. Airplanes and rockets might be a little easier since they would need to carry less weight. Computers tend to brush up against the very limits of physics so it would probably take us more time to develop high-quality smart phones.
There are other "miniature human" posts. Those posts are however about humans much smaller. – Aarthew III – 2016-05-25T23:08:59.630
Also if you want to shrink/grow creatures look up the square cube law. – Aarthew III – 2016-05-25T23:09:41.800
I think my biggest concern is how they defend themselves against the larger predators. At our current size, I would say we are more formidable against the larger creatures, like bears, wild canines, and wild cats. Then again, how did our ancestors avoid sabertooth tigers? Something to consider. – Marion – 2016-05-26T01:09:54.370
1Intellect accomplishes a lot. The lesson for the predators is: messing with the weird taller-than-wide critters means getting hurt and not fed. When you see human style terraforming, cultivated fields and cities, stay away. – Harper - Reinstate Monica – 2016-05-26T02:54:58.853
Not really an answer, but having an intelligent society with creatures that small would make it much easier to become space-faring. Small payloads are significantly easier to get into space! – Thane Brimhall – 2016-05-26T13:24:57.903
About the square cube law, I really think this would drastically change our society. For instance, these small humanoids would be proportionally more resistant, require less food, less oxygen and less water. – Chaotic – 2016-05-27T13:59:04.183