Orchids break down their potting mix in a year or two. At that time they need to be re-potted, which gives you a chance to trim roots and clean up the plant. Another reason to re-pot is a lot of roots growing up and over the edge of the pot. Root-bound orchids may be perfectly healthy and happy, though when they start escaping, it's time for a slightly bigger pot.
Remove an orchid you're re-potting carefully. The old potting mix will be clinging to tangled roots and requires some brushing or rinsing away so you can see what you've got. Try not to damage any of the roots as you clear away the old medium. You can see skinny, brown roots and floppy, mushy ones. Those are dead and may be trimmed with sterile scissors or a sharp knife. The fat, solid roots are healthy, and you can bend them gently to curve into a new pot.
The new pot should be only an inch or so bigger than the old pot. The roots will quickly become slightly root-bound again. A snug fit works well for orchids as it helps to anchor them and they don't spend all their time vigorously growing longer roots and ignoring blooms. If you break some roots while bending them into the new pot, just give the plant some time to recover. Loosely fill the pot with orchid medium, not regular potting soil, and gently tap or shake the pot to settle the medium around the roots. Keep filling and tapping until the plant sits securely in the pot. Refrain from watering it for three to five days so the plant can recover from the trauma of re-potting and any damage to roots.
When you put an orchid in a pot that is too big, you can endanger it. The excessive medium will hold too much water, so the plant will be overwatered, which can rot the roots and kill the plant. Monopodial orchids that grow vertically lose their lower leaves eventually and need re-potting. Put the plant in a new pot so the bare lower stalk is covered and the existing leaves are at the surface of the potting medium. Bend the roots so they wind around inside the pot and up around the buried part of the stalk, if necessary. If you give the plant barely enough room to grow and plan to re-pot in a year or two, you're probably sizing the new pot correctly.