Skinner was born in 1930 in Paducah, Kentucky. He played basketball as a point guard in high school, at Paducah Junior College, and at Presbyterian College, where he earned his undergraduate degree in 1952. His first basketball coaching job was in 1955 at his alma mater Paducah Junior College in 1955. He was hired by head coach Bob Polk at Vanderbilt as an assistant coach two years later after Skinner led his Paducah team to a win against Vanderbilt's freshman squad. He spent the 1958-59 season as the acting head coach in Polk's absence, and led the team to an overall record of 14-10. Skinner succeeded Polk as head coach in the 1960-61 season. With the support of Vanderbilt University chancellor G. Alexander Heard, he pursued the recruitment of African American players for the basketball team. The first player to make the team was Perry Wallace, a local schoolboy star at Nashville's Pearl High School, who enrolled at Vanderbilt in 1966 and first started playing for the team in 1967, becoming the Southeastern Conference's first African American varsity player. Skinner faced opposition from alumni who were opposed to integrating the team; Skinner was primarily looking at recruiting Wallace as someone who would be "a great player, and also a great student, a valedictorian" and that the fact that he was making history was a secondary aspect of the choice. Wallace recalled in a 2009 interview that Skinner practically lived at his house from the time he started trying to recruit him while he was a high school junior. Skinner led the team to the Elite Eight in the 1965 NCAA Men's Division I Basketball Tournament behind a 24-4 record that season, losing to the University of Michigan by two points. Skinner was chosen as coach of the year in the SEC in 1974 by the Associated Press after leading the team to a 23-3 season record, with Skinner receiving seven votes from the 10-member board that selected the winner. Saying that "I don't want to get old being basketball coach", Skinner announced in March 1976 that he would be stepping down as head coach after 16 years and turning the reins over to assistant head coachWayne Dobbs. Skinner led the Commodores to a 278-135 record during his tenure, the most in school history until Kevin Stallings passed him during the 2013-14 season. He was named SEC coach of the year in 1965, 1967, 1974 and 1976. In 2009, Skinner was inducted into the Vanderbilt Sports Hall of Fame.