Turn the current pot of your orchid to the side and gently pull the orchid out. If it is stuck, tap the bottom and the sides of the pot and try pulling the flower again.
Cut out the dead and rotten roots using a sterilized blade. Divide the remaining healthy roots into four sections.
Fill the bottom of your pot with Styrofoam peanuts. You can use any type of pot, but orchids in pots of clay dry out faster and need more frequent watering. Always choose a pot with drainage holes, as contact with standing water will kill the orchid's roots.
Add some Dyna-Rok medium at the bottom of the pot. Place the orchid in the pot. Put sympodial-growing orchids -- such as Brassavola and Cymbidium -- near the pot's edge and monopodials and terrestrials -- like Vandas and Ludisia -- right in the middle of the pot.
Fill the rest of the pot with Dyna-Rok. Check if the orchid is wobbly before adding a label with the orchid's name on the pot to complete the potting process.