Into a CB GroupJive group or into a Joomla usergroup? Joomla usergroups are for controlling access and are a part of the ACL. CB GroupJive groups are purely community groups and have no impact on access or ACL behavior. Both will begin with the following auto action in CB Auto Actions.

Global
Triggers: onAfterUserRegistration, onAfterNewUser
User: Automatic
Access: Everybody

The above will perform whatever action you like after a user registers. So for example to join a GJ group you'd have the following.

Global
Triggers: onAfterUserRegistration, onAfterNewUser
Type: CB GroupJive
User: Automatic
Access: Everybody
Action
Mode: Join Groups
Groups: SELECT_OR_SUPPLY_GROUP_IDS_HERE

Below is an explanation of the triggers you can use to determine where you want this to happen.

onAfterUserRegistration = frontend registration
onAfterNewUser = backend registration
onAfterUserUpdate = frontend edit
onAfterUpdateUser = backend edit

Note CB GroupJive also comes with an Auto Join field type. You can create such a field in CB > Field Management if you want to just let your users select the group to join during registration.