Grost has a long association with college golf, beginning his playing career at McLennan Community College under Hall of Fame coach Jimmy Clayton. He would continue his career at Texas Christian University where he graduated with a degree in psychology in 1979.
After brief stint playing professionally, Grost entered the coaching ranks at Lamar University in 1981. Lamar was a regular participant at the NCAA championships and won three Southland Conference championships during his tenure and Grost was twice conference coach of the year and also won the first of his two GCAA National Coach of the Year honors.
Grost moved to the University of Oklahoma in the spring of 1986 and continued the success that he had at Lamar. The pinnacle of his coaching career came in 1989 when he led the Sooners to the NCAA Championship. He was again named GCAA National Coach of the Year that season. Grost was also named Regional Coach of the Year in 1989 and again in 1992 when he also was honored as Big Eight Coach of the Year after claiming the conference championship. His OU squads won NCAA regionals in 1989 and 1995.
A 2005 inductee into the GCAA Hall of Fame, Grost married Michelle on December 4, 1992. The couple has one daughter, Samantha Jo.