To grill classic barbecue chicken drumsticks, mix up your favorite seasonings to create a dry rub. Dip the drumsticks in the seasonings and massage the spices in to coat them thoroughly. Heat a gas or charcoal grill to medium-high heat and place the drumsticks directly over the heat for about 5 minutes. Turn them frequently so that they don’t get burned. Once you’ve seared the outside of the drumsticks, move them to the cool side of the grill or turn the heat down to low. Cover the grill for 20-30 minutes, then turn the drumsticks over and brush on a layer of barbecue sauce. Let them cook with the grill covered for another 15-20 minutes. Turn them again, brush the other side with barbecue sauce, and cook the chicken for an additional 15-20 minutes. The drumsticks are done if the juices run clear when you cut into them, or when a meat thermometer inserted into the thickest part of the meat reads 165° F (74 °C).
Source: Wiki How