You may want to check out Reiki. It's healing by laying on the hands. I'm trained in it. My mom is a reiki master. It's not based in any particular religion. A christian monk discovered it when a light hit him in the forehead on top of a sacred mountain while he'd been fasting and studying ancient sanskrit texts and dancing and chanting etc etc for about a month.
He opened up a clinic and began healing people for free, but then they would stop taking care of their problems and just come to him when things got bad, so he started charging them. It's pretty popular nowadays. He researched it because one of his students asked him what the healing method was Jesus used, and he couldn't demonstrate.
http://reiki.7gen.com/
I googled and that was the first thing.
The idea is not that the healer or the healee heals, but that the healer becomes a conduit through which the universal energy can restore the proper order and balance in the individual. They say one should be in the right frame of mind, or s/he can take on the disorder of the patient.
Dauer
Oh, and faith plays no part in this. Anyone can be healed. And the healer doesn't need to believe in any particular deity or anything. But some of the history and literature may help to answer your questions.