What do you do if you have clusters of black dots on the surface and bottom of your swimming pool?

That is probably black algae. You need to go to a pool store and have them advise the proper chemical and use of that chemical for your pool. It may take a granular product for white plaster pools. Color tinted pools are another matter and you should use a liquid black algae treatment. And if you have a vinyl liner pool I just do not see how in the world you could get black algae. Black algae comes from not maintaining proper chlorine levels and adjusting the pH.