Testing water in your tank is always a key part of fish keeping, you are after all keeping water and not keeping fish. So long as the water is good, the fish will be too.
The API saltwater master test kit is a good grounds to start testing your saltwater marine tank, it could also be used on freshwater tanks however API do a separate kit for this – API Freshwater master test kit.
In this test kit you get 4 tests; High Range pH (7.4 to 8.8) (160 tests), Ammonia (130 tests), Nitrate (90 tests), Nitrite (180 tests).
The tests work in a very simple fashion – add 5ml of tank water to the test tube and add in the relevant test solution to this, it varies depending on which test you are doing as to which solution you add and how many drops you add to it however all the bottles are very clearly labelled. Then shake the test tube with the supplied lids and leave to stand for around 5 minutes. You then compare to the chart to see what colour the solution you are left with best represents and that is your result.
For a more extensive saltwater test you can use the API Reef master test kit which includes further tests although it does double up on your nitrate tests (given that you only get 90 compared to a lot more on others then this works in your favour anyway).
After seeing various test kits over the years it is clear that there is a balance between accuracy and ease of use however I would suggest that the API test kits give strong results yet ease of use is also taken in to consideration and difficulty level is low.