What are the signs for a stable water? What are stable water level of parameters?
0 ammonia 0 nitrite under 20 for nitrates PH depends on the fish youre keeping but stable PH is better even its out of range then messing with it
"Stable" really means it doesn't change much over time, rather than having any specific parameters.
But the parameters you should aim for are no detectable ammonia or nitrite, nitrate as low as possible (always under 20 ppm), and no big shifts in pH or hardness.
The above is true for either freshwater or saltwater tanks. In a saltwater tank, you also need to worry about salinity levels and (especially if you have reef invertebrates) levels of calcium and some of the minor minerals (magnesium, manganese, idodine, strontium, etc.). Again, "stability" for these levels means they don't change much from day to day or over longer periods of time.
to check it you must get a test kit. nitrates and ammonia should be 0. PH depends on the speccific type of fish. for example, if its a African cichlid then the PH should be 7.5 to 8.5.