Experiments with tinting began in 1890s. The first wide-release Technicolor film was 1922's "Toll of the Sea". By 1939 Technicolor was common for big-budget movies. Introduction of cheap single-strip Eastmancolor in 1950 marked turning point; by 1955 most everything was shot in color.
As far as I am aware, The Wizard of Oz was the first major Hollywood color movie. It may not be the first color movie however. I seem to remember a movie about the Civil War that was a very early version of color film.