Sounds like spider mites, or white flies if they are flying. You can try "NEEM oil" usually just called NEEM. It's organic, but you will likely need to spray often. And spray the undersides of the leaves as well, and trim off leaves that are heavily infested. You may need to ask for it at the nursery, I got some at Lowe's.
P.S. There are many species of spider mites, but control of them is basically the same as far as I can tell...
Mites
Spider Mites And Their Control, HYG-2012-92
Spider Mites Management Guidelines--UC IPM
Twospotted Spider Mite, FC-24-89