Candida is kept under control by maintaining the flora that generate acids, which turn off the Candida growth gene and keep the Candida from going fungal. So prebiotics and probiotics to build up the flora.
And once it 'goes fungal' ... you'd have to take anti fungals
Natural ones like kefir and yucca root.
in addition to a strict low/no sugar/starch diet, right?
Pretty much. There are ways of having some sugar without an issue such as using gymnema as a sugar blocker, and using yucca root to kill the fungi and cut down on fermentation. There are also starch blockers. Simply eliminating sugar/starches will not do the trick since your body will just generate its own glucose. This is why strict Candida diets do not work. The only way the Candida is going to be brought back under control is by making the terrain inhospitable to the Candida, which means restoring the flora for the acids that control Candida overgrowth and avoiding intestinal alkalinizers.
Also remember that the enzymes cellulase and hemicellulase, which many people take to fight Candida will actually make things worse.