Black spots around the base of your fern and on the leaves that are attached to the mounting board are generally your first indications of fungus. If these fungal infections are small and localized, it may be possible to use a sharp knife to cut away the area containing the fungus. Be sure to wash your hands and the blade with rubbing alcohol between each cut to avoid spreading the fungus with subsequent cuts.
Reduce watering and allow your staghorn to dry slightly. Over-watering is almost always the cause of a fungal infection. Allow your fern to dry to the point that some of the newer and more tender leaves begin to wilt. Withhold misting from the plants for several days, allowing the fungus to dry and -- hopefully -- die. Re-water and begin misting when the plant shows signs of stress.
Talk to a knowledgeable expert in your area regarding any anti-fungal agents that may be applied to your staghorn without causing more damage than the fungus is causing. This step should only be taken if the reduction of watering has not solved or mitigated the problem sufficiently. Chemical agents can easily damage staghorn ferns. Use care to avoid disturbing the fuzzy covering of the staghorn's "gripping" leaves -- the leaves holding the plant to its board.
Fertilize your staghorn with fish emulsion or with well-composted humus. Providing your staghorn with a little fertilizer may give it the strength it needs to fight off this infection.