A lightsaber is a pretty unforgiving weapon. Everyone cuts themselves at least once learning how to wield a sword. How common are lightsaber training accidents?
I do not know how common accidents were (I would assume not extremely unheard of because accidents do happen), but I do know that the Jedi of the Old Republic used Training Lightsabers to avoid injuries from such accidents.
Training Lighsabers were used exactly for that purpose. They were lightsabers in all other aspects, except that their low-power made them safe to train with because they could cause less damage. While the Jedi did not build actual lightsabers until they were already competent in their use, actual lightsabers could vary their power output, allowing them to be safer to use for training.