While the origin of communism is debatable, most historians attribute the developements of communism in the 20th century to the writings of German Karl Marx.
In 1848, Marx and his partner Friedrick Engles published The Communist Manifesto, which outlines the principals of communism and how it functions inside an industrialized country.
Communism has exited in many other forms throughout the 1800's and 1900's, most noteably in the western world. The Utopian movement of the early 1800's in the U.S. is a very good example of communal living, along with the somewhat misguided experiments of the 1960's and 1970's. Marx would have made the distinction that these people are "social" communists, not "scientific" communists.