Nelson was born and grew up in Madison, Wisconsin. There she first learned about R&B music from WLAC radio in Nashville. In her teens, Nelson sang folk music in coffeehouses and with a group called The Fuller's Wood Singers and was lead singer in a band called The Fabulous Imitations.

In 1964, Nelson recorded an album released on Prestige Records. It featured blues harmonica player Charlie Musselwhite among her backup band. In Chicago, where the album was recorded, Nelson met and learned from artists such as Muddy Waters, Howlin' Wolf, and Otis Spann.

Nelson moved to San Francisco in 1966, where she became part of the music scene there. Her band Mother Earth played the Fillmore Auditorium, sharing bills with the Grateful Dead, Jefferson Airplane, Janis Joplin and Jimi Hendrix.It was during this period that Nelson wrote and recorded, with Mother Earth on the album Living with the Animals, her signature song "Down So Low," later covered by Linda Ronstadt,Etta James,and Diamanda Galás.