Please describe a good home remedy for bad acne on the back, shoulders, chest, face, and neck?

A better idea. Your question implies rather severe acne. I'm not aware of home remedies that are particularly effective on acne this bad. My suggestion is to have a doctor (primary care or dermatology) evaluate and treat. Acne can be emotionally and physically scarring!
See your MD. But start with a good mild cleanser (i.e. Neutrogena w/ salicylic acid) and otc benzoyl peroxide (just for face). Severe acne like you've described could benefit from treatment by a skilled md.