Who were the first tool users? Tool use is the hallmark of technology, so it's reasonable to say that the first tool makers were the inventors of technology. You can even take it one step further and propose that the first tool makers invented invention itself.
We don't exactly know which species started tool use (the records are filled with phrasing like "tool use is often associated with..."), but our best evidence is found in Australopithecus garhi, around 2.5 million years ago. This occurred in the Olduvai Gorge in what is now Tanzania. The name of this first tool industry is based on the word Olduvai, and it's called: Oldowan.
Realistically, modified tools were probably used before the Oldowan industry. But the Oldowan tools were the first ones that we've found, and are clearly recognizable as tools. This means that they were intentionally modified for use, as opposed to manuports, which were natural objects that were unmodified, but intentionally moved from their original location, like a stone transported for later use.
This tool-defining modification essentially consisted of banging one stone (a hammerstone) against another stone (a core stone). This process resulted in flakes being banged off of the core stone; these flakes were also used as tools.
Here's a recreation of an Australopithecus garhi:
Here's a basic example of an Oldowan chopping tool:
Tool use was limited. Nuts and bones were placed on a large stone that acted as an anvil, and smacked with another stone. Hides were scraped and prepared. Very basic woodworking was done with tree branches.
This ultra-primitive tool use continued for about 1 million years. It advanced into what we now refer to as the Acheulean Industry. The difference between the Oldowan industry and the Acheulean industry is the difference between tools and manufacturing. The Oldowan industry is characterized as impromptu or ex tempore, which means it wasn't really planned. Find stone, bang stone, done.
The Acheulean industry, on the other hand, was planned tool production. It's also notable because the Acheulean era was the longest single tool industry in history. The Acheulean manufacturing process involved Oldowan-style flake removal, followed by further working of the flake with a wood or bone hammer to produce a more finely chipped tool that could be used for slicing.
Here's an Oldowan-style stone tool on the right, compared with the Acheulean-style tool on the left. People often look at the fast pace of modern advancements and remark that technology advances "exponentially". This is true, and it means that while technology advances rapidly now, it once advanced extremely slowly. For example, these two stones represent 1 million years of technological advancement!
The flint knapping Mousterian tool industry came about around 600,000 BCE, then bone/antler tools in the Aurignacian tool industry around 40,000 years BCE. Then came the Microlithic tool industry around 16,000 BCE, with its primitive spears and arrows. Finally the last Stone Age period was the Neolithic Age, around 10,000 BCE, when chipping was abandoned, polishing discovered, and the discovery of farming worked hand-in-hand with the creation of many tools.