The best source of information is Richard Mleczko's chapter in my book. So if you want to keep mudskippers, buying or borrowing a copy will be really useful.
Failing that, the basics are these: Maintenance is closer to that of amphibians than fish. The tank needs to be of a appropriate depth that you can provide a little water (10 cm at most) but lots of climbing area on rocks, bogwood roots, ceramic ornaments and/or plastic plants. The substrate should be a silica sand/coral sand mix, shored up with stones. Filtration can be very basic; a small internal or external canister filter will be ample. Healthy 'skippers spend 90% of their time on land.
The tank needs a secure lid; 'skippers are experts at escaping. Humidity is important, but there should be ventilation via grilles to prevent mould. Avoid using a glass heater, because there's a good chance the 'skippers will be burned as they climb about. If you must use one, fit a heater guard. Otherwise use an undertank heating mat or similar.
Brackish water is essential, but the precisely salinity doesn't matter. SG 1.005-1.015 is recommended.
Diet varies, but most consume insects and some amount of algae. The larger species are accomplished predators on crabs and the like. Choose species with care: all are territorial, and some species aggressively so, to the degree males end up being kept "in solitary" most of the time. Do see my Brackish FAQ for a quick review of the common species. Richard discusses the full diversity in the book. Generally, keep mudskippers alone. They mix poorly with other fish.
Cheers, Neale