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.
I'm also interested in this question. My husband would like to work on the family tree with me. We opened an account for him, but can't link it to the existing record on my family tree - so he can't access or edit our info. Please help.
@Carol Lindsay_2, you can "link up" to the shared, collaborative tree with your deceased relatives. For privacy reasons, profiles for living people are only visible to the account that entered them. This means that you will have a different profile for your husband than what he has for himself, and his profile for you will not be the same one that you see on your own account.
Given this deliberate invisibility, I suggest not investing any time or effort in profiles for the living. Keep track of that stuff offline, and enter simple placeholders or connectors on FS. The only purpose of profiles for living people is to connect you to your deceased relatives.