How do you transplant an orchid?

Soak the orchid's pot in water for several hours, remove the orchid from the pot, shake off any loose soil and then soak the roots in cool water or rinse them under cool running water. Inspect the plant carefully, and divide the orchid if you want to make multiple plants.

For more info- http://www.wikihow.com/Transplant-Orchids

Remove the orchid and re-pot in the next size orchid pot with the recommended orchid medium.

very carefully -- they are hardy but you want to do the least amount damage to the roots, just handle gently.

Are you sure it actually needs repotting? If you feel it does, just gently slide it out on its side and pull away the old orchid bark. However, before doing that, buy new orchid bark and soak it well. Hold the orchid over its new pot and gently sprinkle in the new wet (but drained) bark as you lower it in. There will be little gaps here and there where you will need to stick the new bark in (as it doesn't just "pour in" like soil). With your fingers, squeeze in as much bark as you can so the roots are surrounded by the bark. One word of caution: the first few weeks of watering the orchid, you will see that it's kind of loose in the new bark. By that, I'm meaning that when I gave my orchid new bark, then watered a week later - when I tipped the orchid slightly on its side (to drain any residual water) the orchid slipped right out as the roots hadn't had chance to coil around the new bark and reposition itself. It was okay, no blooms broke but it's something to be careful about. A friend of mine raises over 200 of them and usually replaces his orchids' bark once a year in the Winter. I've learned a few tips from him and now have year-round blooms!