How did Andy Warhol do the silkscreen paintings?

Answer 1

He didn't discover the process. Silkscreen printing was first patented in England by Samuel Simon in 1907, and before that similar processes were found to be used in China from 960--1279 AD. It was introduced to Western Europe in the 18th century but wasn't largely accepted at first. In the early 20th century, people began experimenting with different photo-reactive chemicals to use in the process though it wasn't `perfected` until the early 30s. Andy Warhol popularized the process in the 60s.

Answer 2

Silk screening is just another form of art and when Warhol created his art silk screening hadn't been used much in the Western World. The art comes from Asia and has been used for centuries, but Warhol used it in a new way for his style of art.