You can edit an activist's information by clicking the "Edit" button in the left sidebar when viewing an activist's record. On the edit page you'll be able to edit their personal information (except for email address, see here), custom fields, and tags, and add new source codes. Click "Save Activist" to save your changes.
Note: Changing an activist's ZIP/postal code here (or anywhere else) will cause the activist's address and city to be blanked out. Since they've moved, that information is no longer valid.
If the user you're trying to edit has a full Action Network account because they're an organizer like your or they've saved their credit card information, you will not be able to modify their personal data like name, address, or email -- only they are able to modify it by logging into their account. On the edit page those fields will be un-editable. However, you can still add tag, custom field, and source code information and save those changes.
If this group is part of a Network, if you have the "Overwrite Network Custom Field Data" permission for this group, you will see a checkbox labeled "Overwrite activist's existing data", checked by default. If you leave it checked, when you save your edits, any custom field changes you make will migrate upwards in your network to parent groups, just like custom field changes made by submitting actions do. If you uncheck the box, these changes will stay on your group only and not migrate upwards. If you do not see this checkbox because you do not have the "Overwrite Network Custom Field Data" permission for this group, your edit will behave as if the box was unchecked, so your custom field changes will stay in your group and not migrate upwards.