are you referring to them editing/adding info for living persons or deceased person?
If you adding a family member to an existing family, please review the following article (How do I add a family member to the pedigree in Family Tree?) from the FamilySearch Help Center at https://www.familysearch.org/help/helpcenter/article/how-do-i-add-a-family-member-to-the-pedigree-in-family-tree
After you added the person you can edit and/or add information and find records that might be available for the person.
I think what they are really asking is how to grant access to a family member to see/edit their family data.