Add a record to one table through a form in another table

So One Artist has Many Events.

Can you explain what you mean by this?

"and have it update the Artist Table."  Can you give an example of "update"

If you want to have the details of the child record Events appear on the Parent Artist record, then there will have been a field created on the Artists table for the Events. The field type will be Report Link.  put the field on the Artists form and select the form setting to show the Events on the form.