How exactly do the stabilizers affect the process of Froth floatation method? I mean how do they stabilize the froth in the process?
Bubbles tend to collapse when the liquid that makes up the walls drains away and the walls weaken. The walls can be strengthened by choice of surfactant (and addition rate) and by adding thickeners like water-soluble gums (e.g., xanthan) or polymers or glycerol (also for children's bubbles).
The small particles being floated may act as imperfections that break the walls more easily, so coating the particles with appropriate polymeric dispersants can make the (coated) particles more compatible with the (thickened) wall.
On the other hand, many industrial operations sometimes develop undesirable bubbles/foam which be eliminated by spraying a small amount of low surface tension silicone or non-viscous solvent like isopropanol on the top of the foam. Avoid these if you need to stabilize the foam.