By continually ripping his soul into pieces with the creation of Horcruxes, & experimenting in the dark arts-Voldemort's face takes on snake-like characteristics e.g. red eyes, slits for a nose, etc. It's mentioned during the books that extremely dark magic can warp ones appearance.

How did Voldemort become so disfigured?

It was because of creation of his horcruxes. His soul got mutilated because of it's ripping so many times and thus Voldemort grew less human in appearance. ... Horcruxes are a violation of nature, thus makes Voldemort inhuman.

Why did Voldemort look like he did?

He could charm many people with his looks. The transformation into his monstrous state is believed to have been the result of creating his Horcruxes and becoming less human as he continued to divide his soul. In the films, Voldemort's eyes are blue with round pupils.