Everhart began his undergraduate studies at the Yale School of Art and Architecture in 1970. In 1972 he participated in an independent study program under Earl Hoffman at St. Mary's College. He returned to the Yale School of Art and Architecture in 1974 where he completed his graduate work in 1976, followed by postgraduate studies at the Musée de l'Orangerie, in Paris.
In 1980, he was introduced to cartoonist Charles M. Schulz at Schulz's studios in Santa Rosa, California. A few weeks prior to their meeting, Everhart, having absolutely no education in cartooning, found himself involved in a freelance project that required him to draw and present Peanuts renderings to Schulz's studios.