Complex sentence: In 1941 she made her debut at a club called "Billy's Stable," and in 1948, performing at the Cinderella Club in Greenwich Village, she was seen by Mae West, who gave her a part in a show she was doing.
Split into simpler sentences: In 1941 she made her debut at a club called "Billy's Stable". In 1948, performing at the Cinderella Club in Greenwich Village, she was seen by Mae West, who gave her a part in a show she was doing.