How do we do we demonstrate a #"saturated solution"#?

A SATURATED solution is, by definition, one whose concentration is the same as the concentration at which an undissolved solute would be in equilibrium:

Since a hot solution can hold more solute than a cold one (this does not apply to sodium chloride solutions!), if you see solid at the bottom of the solution flask, the solution is probably saturated.

Undergraduate understanding of saturation is lacking, so it should be noted that saturation is an equilibrium phenomenon and does not imply that the solution can contain all the solute. Supersatirated solutions, on the other hand, are possible; these are solutions that contain an amount of solute greater than that which would be in equilibrium with undissolved solute.

The process of creating a supersaturated solution involves taking a saturated solution, adding more solute to it, and then slowly heating it until the solute dissolves because it is already saturated. If the solution is then cooled down again slowly, it becomes supersaturated; this is a metastable condition, and it can be brought back to equilibrium, to saturation, by scratching the side of the flask or adding a seed crystal.

Supersaturation should be demonstrated quite spectacularly on the web; if you come across a good example, please share it here.

Having said that, let me return to your question. I suggest that sea water is unsaturated with regard to sodium chloride because I could dissolve more salt in a sample of sea water.

A saturated solution is demonstrated by adding solute to a solvent until no more solute can dissolve, resulting in a solution in which any additional solute added will not dissolve but instead precipitate out of the solution.