Judy Garland wasn't born under that well-known name...her birth name was Frances Ethel Gumm. She was born in Grand Rapids, MN, on June 10, 1922. In 1928, she and her two sisters enrolled in dance classes, and by 1934, they had been touring for several years as The Gumm Sisters. By the end of that same year, they had changed to The Garland Sisters.
Eventually Frances changed her name to Judy, and signed on with MGM and Louis B. Mayer. She starred with Mickey Rooney, and knew Clark Gable and Elizabeth Taylor. But finally, in 1938, she made it big in Wizard of Oz. She was 16 years old.
In that movie, she sang the song she's known best for -- Over the Rainbow. However, various things combined so that the movie didn't really make a profit until it was released again the '40s. In 1941, just after she turned 19, she married David Rose, but divorced by 1944. 1942 was the year her first movie came out as an adult star, that being Me and My Gal with Gene Kelly.
Another one of her most successful films came out in 1944, Meet Me in St. Louis. This is my favorite of the Judy Garland movies I've seen so far. She sang three hit songs in it: The Trolley Song, The Boy Next Door, and Have Yourself a Merry Little Christmas. Did you know that's where the latter song started? She does it beautifully. Check it out on youtube...or just watch the movie!
Sometime during that filming, Judy entered in a relationship with Vincente Minnelli, and they were married by the end of 1945. Judy and Vincente had a daughter in 1946 (Liza) and were divorced in 1951. Judy had a very unhappy life, and tried to commit suicide unsuccessfully.
Her adult films aren't as well known, but include The Pirate, In the Good Old Summertime, and Summer Stock. In 1954, she was in A Star is Born.
She died in 1969, from "an incautious self-overdose" of barbiturates. Judy was 47.
You can learn more about her on Wikipedia or in a book called Get Happy: the Life of Judy Garland by Gerald Clarke -- a fascinating, well-written book, but with too much detail in parts.