There are a few rules to remember when changing user groups:
Users can only belong to one group on the Trillian side. Assign user groups that best represent a user's core job function or location.
If a Trillian group is associated with an LDAP group, users can only be moved into the group if they also belong to that group on the LDAP side.
If a Trillian group is not associated with an LDAP group, any user can be moved into it.
Changing a user's group
From Users and Groups, left click the user whose group you wish to change and drag the user into the groups section on the left.
All ineligible groups for this user - according to the rules above - will disappear from view. The remaining visible groups represent viable groups for the user being dragged.
Release the mouse button once you've dragged the user to the desired group.