How can authenticated users of a site join a group implemented using Groups module?
Drupal 7


Download and activate Group.
Activate submodules Group add (gadd) and Group node (gnode).
Click on Group that now appears in your menu bar next to Content (/admin/group). This is the main overview for administering Group, here is where new functionality will appear when you activate more submodules.
Go to Group Types, in a tab on the page (/admin/group/type)
Add a group type, you only have to choose a name
Click "edit permissions" (/admin/group/type/manage/partner/permissions)
Activate suitable permissions. "Outsider" are logged in users that are not part of the group. Add at least view and add permissions for one content type for members, and "View group" permission.
Go back to the Groups start page (/admin/group)
Create a new group
Click on your group name, then click Add member
Add some members
Log in as one of those members, go to your account, click the Group tab, click on "view group"
Add some content


Now you have the basics of a group. Users, content, permissions and some ways to interact. Look through the rest of the tabs on all pages you visited, go into the detailed settings screens, activate more submodules, group roles, group permission etc. Extend using the group api hooks. Set up a suitable user interface using standard tools (views, VBO, rules, fields on the group). 

For other settings you can visit following urls :


https://www.drupal.org/node/2711123
https://www.drupal.org/node/2711049
https://www.drupal.org/node/2711119
https://www.youtube.com/watch?v=w2Ol19OzNAQ


Drupal 8 

Watch this video for a excellent and complete use-case configuration. 

Hope this will clear all doubt.