Born in Williams, Oklahoma, Martin threw and batted right-handed, stood 6 feet 1 inch (185 cm) tall and weighed 185 pounds (84 kg) during his active playing career.

With the reserve clause binding players permanently to the U.S. teams in "Organized Baseball" who held their contracts, the insurgent Mexican League induced players such as Martin, Sal Maglie, Mickey Owen, Lou Klein, Max Lanier, Danny Gardella and others to leave their clubs — in Martin's (and Lanier's and Klein's) case, the pennant-contending but notoriously low-paying St. Louis Cardinals — for greater riches south of the border.

As part of the lawsuit, Martin and Lanier had requested a preliminary injunction allowing the "jumpers" to immediately return to their former major league teams, per the reserve clause.

He became especially famous as a proponent of the split-finger fastball, which he taught to Cub farmhand Bruce Sutter, who mastered it, became a dominant relief pitcher in the 1970s and 1980s, and was elected to the Baseball Hall of Fame in 2006.

In 1979, former Cub shortstop Don Kessinger, named the playing manager of the Chicago White Sox, asked him to be his pitching coach, but Martin was ill with cancer.