Begay's work included depictions of everyday life, often with scenic backgrounds including Monument Valley and Shiprock.[4] After winning a fellowship, Begay worked for a year in the 1950s studying with illustrator Norman Rockwell at his workshop in Westport, Connecticut. Begay's work often shows this influence.[4]
Begay attended Phoenix High School.[5] He lived much of his life in Shiprock, New Mexico. In addition to exhibiting at galleries and fairs, his work was sold in local trading posts.[6]