Like many Practical Life activities, this is something you teach your child to do naturally. M likes to do things on her own, and this is no exception. She can open and close the toothpaste (she still needs some help squeezing the toothpaste onto her toothbrush), wet her toothbrush, and brush her teeth. I typically do a quick follow-up brushing, but she is pretty thorough on her own now.
See more Practical Life activities here.