How to assign users to a group
From a permission point of view, (instead of groups) these are called "roles" in Drupal. (From a content-user-access point of view there is the Organic groups module, but that's another story.)

You can administer roles at admin/people/permissions/roles. You can mass assign users to roles at admin/people (Update options - Add a role to selected users).

All registered users automatically have a role called "authenticated user", so there is no need to duplicate that functionality.

For more info check out "Managing access control with permissions and user roles" at 
https://drupal.org/node/22275