Teaff played high school football at Snyder High School in Snyder, Texas and collegiately at San Angelo Junior College (now Angelo State University), and McMurry University in Abilene, Texas. When McMurry head coach Wilford Moore went on to coach Lubbock High School in 1956, Teaff became his assistant. He then moved on to be an assistant at McMurry from 1957 to 1959.