Nelson was born in Baton Rouge, Louisiana. He began teaching acting in New Orleans, Louisiana in his early twenties after attending Louisiana State University and graduating from the North Carolina School of the Arts in Drama. There, he was a classmate of Broadway and film stars Tom Hulce and Terrence Mann. He later moved to Houston, Texas where he taught at Patrick Swayze's mother Patty's studio. While in Houston, he found his first major film role in Joe Dante's Piranha (1978). He later appeared in two other movies directed by Joe Dante, which are Innerspace (1987) and Gremlins 2: The New Batch (1990; as he played Wally).