Once you have created a Group, any time you are viewing an individual contact's profile, all of the groups (separated by those they're members of first, and those they aren't second) will be listed on the right-hand side.
Select or deselect the checkboxes next to the group name if you want to remove someone from a group or place them into another group.
You can also add and remove contacts from a group page. Let's use the "Alumni" group as an example.
From the Alumni group's page, you can add a contact using the dropdown box.
To remove a contact from the Alumni group's page, click the "x" next to the person's name you want to remove from the group.