Black dot acne. Those black dots are most likely open comedones, the fancy words for blackheads. These are actually brown, and turn color because enzymes in the skin turn them that color. It is not from being dirty. Gentle washcloth action in the shower, exfoliants like retinol and Retin-A and acne cleanings at your dermatologist's office will help.
Home or Professional. Cleanse, tone, and exfoliate. If all else fails see an esthetician who will properly extract the black head.