In the admin area, search for the household you want to edit…
If you click on the last name, it will bring up the whole household, with various edit links, including an Edit Address link
If you click on the address it brings up the address edit screen
If you click on a first name, you can edit that person.
On the whole household screen (accessed by clicking on the surname) there is a Move link. That will allow you to create a new household at the same address with that person, or add them to a different household.
On the front end, you can use a shortcode to display the address list and there is a register shortcode too.
If you view an address list an edit link will appear against your household for non admins and on every single household for admins.
To not be shown on the address list edit the address and check the private checkbox at the bottom.