How long will it take for breasts to dry up after I stop breastfeeding?

Depends. Some women will dry up after a week, some a month, some still leak drops of milk months later. It is all individual. Be prepared for engorgement discomfort when you stop. Binding the breasts with a tight bra, ace wraps, and sometimes cold cabbage leaves have been known to help. Resist the temptation to pump, as this only tells your body to make replacement milk.
It depends. If you are weaning your baby it can take several days for the breasts to stop producing milk. Important to remember any stimulation of the nipples can continue milk production, binding the breasts can be painful. "the nursing mother's guide to weaning" by huggin+ ziedrich has many helpful tips and suggestions. Support groups such as the nursing mother's council and la leche league also helpful.