Your contact's Overview screen contains a Tag Groups section in the Know Your Client area for the contact. Below is an example of this section:
This area will display any Tag Groups that the contact is currently a member of.
The Add button in the upper right corner will allow you to include the contact in additional Tag Groups (as well as to remove them from groups they are currently members of or create new Tag Groups on the fly to place them in):
The Actions menu for Tag Groups displayed on a contact's Overview will allow you to remove the contact from that Tag Group or to view all of that Tag Group's members: