To add a Shared Address to a user:
  1. Navigate to Core.
  2. Select Users > Edit User Profile Data.
  3. Search/select your user and click on their name
  4. Click on Contact Card
  5. Scroll down and locate the Address section 
  6. Click Add.
  7. Click the Select Existing Address radio button.
  8. Select the Address Type from the drop down.
  9. Click Next.
  10. Select the Share radio button, to make this a shared address, -OR- select Copy, to make a new instance of the address.
  11. Select the radio button to the left of the address you want to add.
  12. Click Save & Exit
To the left of a shared address will be a 'linked' icon,. Hover your mouse over the icon to show who is sharing the address.
share symbol

With the October 2016 release, a constituent must have a relationship with all other constituents already sharing an address in order to have the shared address added to their profile. The option to Select Existing Address will be unavailable if the constituent does not have a relationship with all constituents sharing the address.
See Why can't I add an existing address to a user's profile? for more information.