Here are several easy ways to keep orchids in trees.
If you are in an area that never freezes you can wrap the roots and tie them directly to a tree branch.
This photo shows the technique tying them to a grapevine branch rather than directly to the tree. The plant is removed from the pot and all potting medium is removed. Then the roots are wrapped with sphagnum moss and the moss is held in place by wrapping with fishing line. Fishing line is then used to tie the wrapped plant to a branch.
Even here in Florida where we can leave the orchids outside year round most of my customers prefer the orchids mounted separate and hung from the tree branches by a hook as shown in the photo. This enables you to bring the orchid inside to enjoy the plant when it is in flower and bring it back outside when the flowers are done.
Another method is to place any potted orchid in a hanger and then hang it from a tree branch, I prefer the double sided hangers as shown in the photo. Plants lean over and fall out too easy in single sided mounts.