Why and how are azeotropes formed?
If we prepare a liquid-liquid solution of equimolar concentration, we know that the more volatile liquid component will have a greater composition in the vapour phase. 

Let us keep increasing the concentration of the less volatile component in the solution. Initially, even though the solution is richer in the less volatile component, the vapour phase will be richer in the more volatile component but there will come a time when the vapour phase will be richer in the less volatile component. It may so happen that the composition of the vapour phase becomes equal to the composition in the solution phase. At this point, azeotrope is formed. 

Note that if azeotrope is formed at all, both the solution and the vapour phase will be richer in the less volatile component.

Take the example of ethanol-water solution.
Ethanol boils at 78.4 °C, water boils at 100 °C. Azeotropic mixture is obtained at about 95% percent of ethanol. Note that the less volatile component is present in greater amounts when the azeotropic mixture is formed.

I will keep adding more to it as it comes to me.