Born in Washington State Martin was neither Irish nor Mexican. He grew up in a predominantly Mexican neighborhood in West Hollywood where he became adept at imitating the Latino speech patterns of his playmates.

Richard began working in films as a receptionist at MGM in the late 1930s. He began appearing in films under contract to RKO in the early 1940s. Martin created the character of Chito Jose Gonzalez Bustamonte Rafferty, the Irish-Mexican comic sidekick of cowboy star Tim Holt, in the 1943 film "Bombardier". He played the character in a series of 29 films through the early 1950s.Martin married actress Elaine Riley, who co-starred with him in several films.