Start by soaking it – a long bath or a hot shower would be good.
Soften the skin using baby oil or a gentle bubble-bath.
Squeeze some exfoliating body (or face) scrub onto a wet cloth.
Rub the cloth against your neck in small circular motions, going over the same area several times before moving onto the next.
Rinse your neck and pat the area dry with a towel, rubbing it gently if any dead skin comes off.
If you’ve had a dirty neck for a long time, it’s probably going to take more time for you to get it clean again. Try repeating the cleaning process every time you shower.
Get into the habit of exfoliating whenever you wash, and your neck should stay clean in future!