Missing teeth and tooth decay were surprisingly uncommon. Studies of skulls have shown that an average medieval person had some decay on 20% of their teeth as opposed to 90% seen in some 20th century populations. Medieval Europe had very limited access to any kind of sugar while diseases such as scurvy were largely absent. People’s diet was generally calcium rich and nutritious enough to avoid nutritional deficiencies. Scurvy is actually surprisingly hard to contract and only became a major issue in the age of long distance voyages. Many people certainly lost teeth due livestock related accidents but they weren’t anymore prone to them than modern farmers.
However it was more common to have incredibly worn teeth. In medieval Europe most of your daily calories came from bread which was ground using a mill-stone via wind, water or horse power. Mill-stones tended to discharge a lot of gravel which meant that most people’s bread contained a measurable quantity of grit. The effect of this was that teeth were ground down, and serious dental conditions like abscesses were very common. It seems probable that large numbers of people suffered from constant dental pain.
If your tooth needed to come out there were a few options. Doctors were a off the table if you were poor and would only diagnose your problem. They left the work of tooth extraction to barber surgeons who used the tried and tested grab and pull method. This is pure speculation but I imagine quite a few people just put up with problems rather than facing a man with pliers and no anaesthetic. It takes a huge amount of effort to remove a tooth, today surgeons will sometimes kneel on patents’ chests to be in optimum yanking position. Now imagine having up deal with that while fully conscious!
There were also quack doctors who would appear at fairs and markets. A common folk belief held that toothache was caused by worms. A well worn trick involved the doctor using slight of hand to remove a worm from the patients mouth. Other treatments involved blood letting (because why not) and various herbs which might be prescribed by a woman with knowledge of medicinal herbs. There were also charms, amulets and spells to heal your teeth if you were unwilling to entrust a surgeon with your life.
I found this question from a couple of years ago, the top comment by /u/sunagainstgold touches a lot on your question.