How do we do we demonstrate a #"saturated solution"#?
You want an experimental protocol? I don't know the equipment you have available. I can propose definitions..
By definition, a SATURATED solution is a solution whose concentration is equal to that concentration which would be in equilibrium with undissolved solute:
So if you see solid at the bottom of the solution flask, the solution is likely saturated. Often we specify a temperature, in that a hot solution can hold more solute than a cold one (this does not apply to sodium chloride solutions!).
Note that saturation is an equilibrium phenomenon that is poorly understood at the undergraduate level. It DOES NOT MEAN that the solution can hold all the solute that it can. Why does it not mean this? Because, SUPERSATURATED solutions are also possible; SOLUTIONS that CONTAIN AN AMOUNT of SOLUTE GREATER to that which would be in EQUILIBRIUM with undissolved solute.
How do you form a supersaturated solution? At room temperature take a saturated solution, ADD more solute. Of course, the solute will not dissolve because the solution is already saturated. But heat it slowly, and the solute should go into solution. If the solution is then cooled back down slowly, the SOLUTION is NOW SUPERSATURATED; this is a metastable condition, and the solution can be brought back to equilibrium, to saturation, by scratching the side of the flask, or adding a seed crystal.
There should be some quite spectacular demonstrations of supersaturation on the web. If you find a good one, post it here.
All this being said, back to your question. I propose that sea water is unsaturated with respect to sodium chloride, inasmuch as I could take a sample of sea water and dissolve more salt in it.