Saltwater fish are kept the same as fresh with the exception they are in salt water. The big problem associated with marine is the PH & ammonia. In a freshwater tank with a neutral PH (PH of 7.0) or acid PH (PH below 7.0) ammonia is not a problem. Seawater has a PH of 8.4 and any ammonia produced is very toxic at this high PH. In acid water ammonia is harmless but as the PH goes above 7.0 ammonia becomes more toxic. Thus the reason it is important to cycle a marine tank before anything goes in it.
After the tank has cycled you maintain it in a similar manor to freshwater tanks. You monitor the ammonia, nitrite and nitrate levels. You keep the PH at 8.4 and you add freshwater to replace evaporated water thus maintaining a steady salt level in the tank water.
If you keep live corals then you should also monitor calcium and phosphorus levels. Generally phosphate levels increase on par with the nitrate so if you do regular water changes you keep both nitrate and phosphate down.
Hard corals (corals with a calcium based skeleton) require calcium to grow. If there is not enough calcium in the water these corals will not grow and may actually die.
Filters get maintained the same in salt as fresh. Wash the filter materials out in a bucket of tank water about once a month. You can gravel clean the tank to remove sediment and debris.
Water changes can be done with natural seawater (from the beach) or artificial marine salt. Artificial marine salt is available from any aquarium shop and you add an amount of salt to a container with freshwater. You aerate the mixture for a couple of days and make sure the salinity is right. Then the freshly made seawater, or natural seawater can be used to do a water change on the tank. To water change the tank you simply drain out a percentage of the water and replace it with clean salt water.
NB: make sure you use a proper marine salt to make up artificial seawater. Swimming pool salt, rock salt, table salt, etc are not suitable.
You feed marine fish on frozen, dry or live food and have a light on their tank in the evening so you can see them.
Many marine fish come from water with lots of strong currents. Therefore it is a good idea to provide some sort of water movement in the tank via powerheads, powerfilters, or airstones.