When adding a new contact (or editing an existing contact), you can manually add them to an existing group. Do so by selecting from the "Select a group" dropdown on the "New Contact" screen.
Add a contact to as many groups as necessary. Once a contact has been added to a group, you'll see the groups listed in the same area. Hover and click on the "X" to remove the contact from that group.
The groups available in the dropdown menu are comprised of any added using the "Groups" module on the lefthand side of the CityGro portal. Manage existing groups or add a new group by navigating here: