I like to float mine, plant down, mount up, in water for 15 to 20 minutes before breaking them down.
I've had good results by firmly, but carefully, grasping the crown of the plant. Basically, where the roots meet the stems. Grasp the crown and gently rock it in little circles, gradually loosening it.
You can be rougher on the roots than you might think, and still have success. I prefer small starts, so when I get an orchid in, I will often break it down into multiple divisions, right then and there.
I also really go into the rootwork, removing virtually every bit of sphagnum, and cutting away all the dead roots.
You might be surprised to see how much rot is locked up inside an orchid root mass. As long as I'm in there, I perform surgery, hacking away all the old stuff, and making space for crisp, new, white roots to lock it firmly to it's branch/wall.
Do not overlook the rather nontraditional method of using super glue gel to attach orchids. I've yet to see other people doing it, but it works great. I used to farm live coral, which is much more sensitive than orchids, and I used a LOT of BSI Thick superglue. (any true superglue will work, but the thicker, the easier it is to work with.) It never harmed even the most delicate of corals, so I gave it a shot in my viv. It allows me to mount orchids in places that would have been impossible any other way.