Just wondering.
For much of Europe the answer was the Dental Pelican This only slightly barbaric tool would often be combined with great amounts of alcohol and anybody willing to pry your tooth out.
While they weren't called dentists way back when it wasn't uncommon for a travelling salesmen to realize that lots of people needed a tooth extracted. An enterprising man with a set of these tools a chair and a willingness to rip teeth out of people's mouths could make a decent living for himself. In larger towns barbers would often act as surgeons and tooth extractors.