Dick Conner was born in Colorado but grew up in Salt Lake City, where he started diving. In 1951 he visited Southern California for several months with his parents and stayed there for his senior year of high school so he could train with Pasadena Athletic Club and Bud Lyndon. He won the Southern California High School Championship that year and earned a scholarship to USC. As a student at Southern Cal, Conner was undefeated in three years of Pacific Coast collegiate competition. Conner placed third at the 1955 AAU Meet on the platform and was second at the 1956 Olympic Trials. At the Melbourne Olympics Conner was in the lead after the qualifying round, but eventually finished in third place. Conner also represented the United States at the 1959 Pan American Games, where he placed fourth on platform.