There isn't much you can do about it now. Yes, the tail becoming black means it is dead. That snake had several bad sheds where the end of the tail never came off during a shed. All the sheds after the original where the end of the tail did not come off were repeated. The next sheds finished where the original bad one did. This caused the end of your snakes tail to have the blood circulation cut off. Due to the blood supply being cut off the end of the tail died.
There really isn't much you can do. Just wait, it should just fall off. In the future, maybe try misting the snake with warm water a couple of days while he/she is in shed. This should provent skin from remaining on the snake after a shed.