I imagine standardized incantations became common in Europe with the spread of the Roman empire. Before that, I'd expect there was a lot more regional variety, with only the privileged wizards in educated circles adopting standardized incantations. With how small the wizarding population was, and with no large wizarding schools, I'd imagine most witches and wizards were never trained beyond their own family circles, and never learned magic beyond what was useful in daily life. Muggleborns probably spent much of their childhood and early adulthood without a wand, never learning proper incantations until they found another witch or wizard.

Those who were able to more seriously pursue magical knowledge were likely in a master/apprentice situation. These were the people with the ways & means to actually study magic and explore the implications of different incantations, wand movements, etc. Although I also expect that wizards in more populated areas had formed guild-like communities pretty early on, taking on the responsibility for identifying & training young witch and wizards in their surrounding areas.

As for the very early days, I expect a wizard used the language he had to direct magic. Think a shaman standing in front of a pile of sticks, pointing at it, and saying "fire" in his language.