The basic process by which opening of stomata takes place is by endosmosis.Endosmosis causes an increase in turgidity in the guard cells thereby causing its opening.
The closing of stomata is achieved by exosmosis which makes the guard cells flaccid.
HOW DO THE REGULATION TAKES PLACE IN PLANTS:
If you read the theory proposed by Levitt from the given [link]
,in which the theory is explained in simple steps with diagrams, you will understand that $K^+$-$H^+$ pumps is the main driving force which regulates whether endosmosis or exosmosis would take place.
When the concentration of $K^+$ increases in the guard cells there is osmotic influx of water from the surrounding epidermal cells and thus 'endosmosis' occurs causing opening of stomata.
Similarly when concentration of $K^+$ decreases there is osmotic loss of water from the guard cells to cause 'exosmosis' and thus closing of stomata.
WHY THE STOMATA CLOSE IN SALT WATER:
When the guard cells of the stomata are open it means they are turgid due to endosmosis.However when such a turgid plant cell is placed is in salt water(hypertonic solution) the latter having a higher concentration of salt ions than the guard cells causes the loss of water from the guard cells.
Thus the salt water is inducing exosmosis to take place in the guard cells due to which they become flaccid and close.