1. You must be a "Site Owner" to do this.
    Log into SharePoint on the web and navigate to the SharePoint site url
  2. In the top right click on the gear icon (after it eventually loads)
  3. Select "Site permissions"
  4. Click on "Advanced permissions settings" at the bottom
  5. Click on the "{site name} members" group.
  6. Check the box next to the group corresponding to the AD Domain Group ("{site name} Share") containing the standard users.
  7. Click on "Actions" and select "Remove Users from Group" and click OK to confirm
  8. Use the browser back button to go back to the Site Permissions page
  9. Click on the "Grant Permissions" Button at the top
  10. Invite people: add the ("{site name} Share") group
  11. Click on "Show Options" and Deselect the "Send and email invitation" 
  12. Change the permission level to "Read"
  13. click "Share"
  14. Navigate back to the sites' document library (click on "Documents" on the left in the navigation pane)
  15. On each of the Root Folders:
  16. Select the "..." and click on "Manage Access"
  17. On the "Manage Access" popup window, select the "..." at the top and click Advanced Settings
  18. Click on "Stop Inheriting Permissions" button on the top bar, then "OK" for the popup "You are about to create unique permissions for this folder."
  19. Check the box next to the group corresponding to the AD Domain Group ("{site name} Share") containing the standard users.
  20. Click on "Edit User Permissions" on the top bar
  21. Check the box for "Edit", deselect the others (ie. Read), and click OK