I would take a look at
this and
this page.
Isolate the female in a separate breeding tank, maybe 5 or 10 gallons (smaller might be too cramped for the female and will experience quicker deterioration of water quality; the larger the aquarium, on the other hand, the harder to observe the larvae).
This should have filtration (established sponge filter would be best) until the eggs begin to darken, at which point you should switch to an airstone. Once the eggs have hatched, you should carefully return the female to the original aquarium and add marine aquarium salt until salinity in the breeding tank is 12 ppt. Some aquarists find it necessary to restrict the flow of the airstone by tying a knot in the tubing or crimping it with a heavy clip; as long as there's decent circulation and water isn't being splashed from the surface, you should be fine.
Keep temps a constant 76-80.
They should start feeding on newly-hatched brine shrimp, though I there are commercial powder foods out there which might also be suitable.
Waste should be carefully siphoned off the bottom (take care not to suck up any larvae) and the removed water replaced with water of the same salinity. Evaporation, on the other hand, should be topped off with distilled water if possible, but plain freshwater will do.
Some people choose to keep the tank light on 24 hours a day, but I'm undecided as to whether this is beneficial.