Go to the Group Membership tab on the Edit User page to see the list of current assignments of the user.
How to Add a User to a Group or Organization
Here you can move a user to a different organization. Just select it in the Organization menu.
You may add a given user to other groups by selecting corresponding checkboxes or remove this user from groups by deselecting them.
How to Create a New Group
You may also create new groups in the same window: