Move the orchid to a location where it gets filtered light because direct light can cause spotting. Isolate the orchid from other orchids in case it is a fungus. Wait a few days to see if the black spots change. If the spots get larger you have a fungus.
Cut off leaves that have extensive black spotting using a clean, sharp knife. Discard the leaves and sterilize your knife before using it on another plant.
Spray a orchid fungicide on both sides of the leaves. Leave the plant for one week to see if the spots disappear. If they return, spray the leaves again.
Water the orchid sparingly since this encourages fungus to grow. Do not let it dry out completely, just cut back on the waterings and don't let it sit in water. It is also beneficial to decrease the humidity in the room as the plant recovers. Water the plant as usual once the fungus is gone.