These ferns are epiphytic, which means they grow mounted on plaques or other substrates. They have two distinct leaf forms—small, flat leaves (known as shield fronds) that cover the root ball structure and take up water and nutrients; and green, pronged antler fronds that emerge from this base and can reach up to three feet in length indoors (and larger in the wild).
The key in helping your staghorn fern thrive is to mimic its natural, sub-tropical conditions as best as you can. Dapples of sunlight (they're used to growing on the bark of trees beneath a canopy of leaves) and lots of moisture will be two essential ingredients to a happy, healthy staghorn fern.
Staghorn ferns prefer to be kept in a location that boasts consistent, shaded light. That being said, they can handle more sunlight if given enough water, warmth, and humidity. Just be cautious about allowing any direct rays to hit the fragile fronds, as they can burn easily.
Proper watering is an essential component of a staghorn fern's success. They'll need frequent watering, but the base should be allowed to dry out in between—about once a week in warmer climates or during the summer months, and once every two to three weeks in cooler months. For easy watering, remove your fern and its mounting from the wall (or wherever it's hung) and soak in a sink filled with water for 10–20 minutes, or until the roots are fully saturated. Allow to drip dry before rehanging.
If you notice the fronds have begun to brown or blacked towards the base, it's likely your plant is being over watered. Likewise, if the tips of the fronds begin to brown or wilt, it probably needs to be watered more frequently.