How can a user join a group in Drupal Commons?
In your Drupal admin area, go to "Administration → Structure → Content types → Group → Manage Display → Default" (/admin/structure/types/manage/group/display).
Set column "Format" for field "Group" to "OG subscribe link".


Your groups will now display a "Subscribe to Group" link on the groups' pages. This only applies for users who have the privilege to request membership to a specific group (which can be set in both the global OG permissions, and can be overwritten per group).