I feed them an assortment of insects and the same mixture of greens, veggies and fruit that I feed my turtles.
The discovery happened like this...the crickets were breeding in their cage so I decided that if I fed the crickets well, I would have a mini-eco system going there. It worked....but I was surprised to see the anoles go down to eat the "salad" that I put in the cage for the crickets. I didn't have to add a cricket for years. I would simply wet one area of the cage down when I wanted the crickets to breed and dry it out to stop them from over-running the cage.
Another thing that happened....I couldn't get them to produce eggs for the first few years that I had them (and they were old enough)...but once they expanded their diet to include the "salad" they produced eggs.