Thaw the turkey if frozen. This takes at least four days, and should be done in the refrigerator. Put it into the pan you'll roast it in to catch any leaks. After it thaws, remove that metal or plastic thing holding the legs together (a pair of pliers is essential, I find). Remove the giblets and neck from the cavity, and clip off the wing tips. (You can use these parts for making stock for the gravy.)
The day before, marinate the turkey in a brine. The standard proportion is one cup of salt to one gallon of water. Make enough of this to completely cover the turkey in an ice chest with an unopened (so as not to dilute the brine) bag of ice to keep everything cold. The brining process takes twelve to eighteen hours for a fifteen-pound turkey. Another method is to put the turkey and the brine solution inside a leakproof plastic bag, and put it into the refrigerator.
The morning of the day you want to serve the turkey, dump the brine and rinse the bird very well inside and out with cold water. Season it with salt (yes!) and pepper. Stuff the cavity with all the other ingredients, and tie the legs just tightly enough to keep everything inside.
Fire up the grill with charcoal and sugar cane or smoking wood, soaked in water and then shaken dry. Put the turkey into an aluminum pan with a loose tent of foil over the top. Place the turkeys as far as possible away from the fire, and hang a curtain of foil down to ward off direct heat. Any heat that gets to the turkey should arrive in smoke.
Close the cover. Add coals and cane at intervals to maintain a temperature of 200 to 250 degrees inside the pit. It takes six to seven hours for the internal temperature of the turkey to reach about 180 degrees. Use a meat thermometer for this; the useless pop-up plastic indicator will pop only when the turkey is overcooked.
Take the turkey out and put it on the table to rest and cool before carving. Although it may be tempting, don't use the drippings for the gravy. They reduce so much during the long cooking time that they become impossibly salty--the only evidence of excessive salt in brined dishes.