Users/Group

Here you can search for users that are inside your contact list or groups that you are apart of. To add to the Users/Group list, click into the search box, start typing the user or group name, when found click the user or group you wish to add and then click the + button to add to the list.

You will then be able to adjust the permissions, the permissions added are instant so there is no need to save the page to have them applied.

View
This user will be able to only view the group and have no edit rights.

Edit
This user will be able to view and edit the group.

Inherit
When a group is added, inherit allows you to inherit the permissions of users added to that group. For example, if 'user 1' has edit rights inside the group 'Group', when the inherited checkbox is checked, 'user 1' will also be able to edit this group.

Remove Permission
The - button at the right of the user or group will remove the permission from the group.

Owner

If you have edit permissions to the group (which you will if you can see the sharing tab), you can change who owns the group by clicking the Change button, entering a user from your contact list in the dialog and then clicking Update, this will apply the owner change.

Audit - Permission Check

The Audit - Permission Check button allows you to view who has access to the group. To do this click the Permission Check button, either enter in a user from your contact list and click the user when you see it, or select 'Public' to determine whether the public has access to the group.