Buff was born in Speicher, Switzerland, the son of a farmer. At age fourteen, he apprenticed with a baker, and later entered trade school to study lace design. After studying briefly in Munich, he emigrated to the United States in 1905, first working in Wisconsin as a sheepherder. In 1907, Buff found his way to Los Angeles where he took various jobs as a gardener, baker, cook, and house painter while also painting scenes in oil on canvas in his spare time. From his work as a house painter, he eventually established himself a contractor, but continued to teach himself to paint. Buff had his first one man show at the Los Angeles County Museum of Art in 1920 and he exhibited extensively around southern California over the next two decades. He was a member of the California Art Club and associated with important early West Coast landscape painters such as William Wendt, Guy Rose, and Jack Wilkinson Smith. However, Buff drew little artistic inspiration from these "California Impressionists." He had cultivated an angular, modernist style using strong color applied in a pointillist manner, but laid down in large color blocks more in line with post-impressionism. His landscapes emphasize geometric forms usually assembled in flat layers. His mountain landscapes, in particular, had an architectural feel. Buff also produced color and black-and-white lithographs, mostly of landscape subjects. In the 1920s Buff developed close friendships with the modernist architects Rudolph Schindler and Richard Neutra, and the artist, Maynard Dixon. Undoubtedly, he shared a much greater aesthetic affinity with these artists than with most of his California contemporaries. He accompanied Dixon on painting trips through the desert Southwest, and executed two mural commissions with Dixon in the late 1920s. In 1922, Buff married artist and museum curator, Mary Marsh. In 1936 they began collaborating on children's books which Mary wrote and Conrad illustrated. Nature and the environment, Native Americans, and Switzerland constituted the themes of most of the thirteen books they published together. Several were nominated for Newbery and Caldecott awards. As Buff's work matured, it became increasingly abstract. Where he had once emphasized basic shapes in the landscape, he later came to exaggerate them to create two-dimensional patterns, rendered in increasingly bright and simple colors. Although he retained his pointillist technique, the strokes became much broader and, often, unconnected. He loved the clear air of the desert and, through color, attempted to capture its effects on the red rocks of his favorite places such as Zion, Monument Valley, and the Colorado River.