Well. First welcome to the site. Is this your first salt water tank or first tank on your own.
Was this tank running at the store when you purchased it?
First you need to do some research. Look on this forum for first time, new to hobby, if your on a laptop look at the first threads on the forum. There is a lot of information out there so ask questions.
Is there a brand name on the tank? You can try switching the bulbs and that should tell you if its the bulb or the socket. There should be two switches on the unit. Photos would help a lot.
Saltwater - in general saltwater is much more demanding than a freshwater tank. Feed minimally and I mean minimally. A tank that small can crash easily, look it up in the search and you will understand the issue.
Did you get a test kit? Also with a tank that small you should test twice weekly for ammonia, nitrite, and nitrates. If you start seeing any of these you should do a water change and then ask questions on here.
Tanks need to cycle so it is important to know the history of the tank. How long was it running before you purchased it? Look up tank cycling and that too will give you tons of information.
There should be a powerhead in the tank, some type of filter, lights, and possibly a heater. Don't need a heater if your temp is constant around 78 degrees.
Again welcome good luck and ask questions and research.