You use lace release to spray on the piece to loosen the bond for both tape and glue. Wait a few minutes, then slowly pull your piece off. If you've done it properly, most of the tape and glue will be on your scalp.

You use a "glue melter" I use something called Amber, I spray the base with it and let it soak in cold water for a few hours. I don't do this often, only if I cant get the residue off the base. I also use Amber to spray on my scalp to remove the residue there.

Use a glossy magazine instead of a mirror, its easier and there is no clean up.