Grills are merely outdoor ovens. The technique used for grilling a whole chicken works for turkey, but you need a large barbecue -- at least 22 1/2 inches long. Gas grills typically accommodate a large turkey without issue. Another concern is weather. If you're grilling turkey in cool weather, expect it to take about 14 minutes per pound, or about 3 hours. When grilling in temperate weather, you can expect about 2 to 2 1/2 hours of cooking time.
Remove the giblets from the turkey.
Mix 2 cups of kosher salt and 1 cup of sugar with 2 gallons of water. Add aromatics, such as a few bay leaves, crushed garlic cloves, red-pepper flakes and black peppercorns, and mix the brine again.
Place the turkey breast-side down in a plastic- or stainless-steel food-safe container and pour in enough brine to submerge it. Mix more brine if necessary. Cover the container and brine the turkey for 24 hours in the refrigerator.
Take the turkey out of the brine, pat it dry with paper towels and let it sit uncovered overnight in the refrigerator. Set the turkey on a wire rack in a deep pan to contain the dripping brine.
Spread out about 50 coals after they ash over. If you have a gas grill, set the burners to medium high. Open the bottom damper; open the lid's vent halfway. Close the grill, and let it heat for 30 minutes.
Add spices and vegetables, such as onions and celery, to the turkey cavity; tie the legs together with twine. Coat the turkey with vegetable oil. You won't eat the vegetables -- they fill the cavity so the turkey cooks evenly.
Transfer the turkey to a wire rack set inside an aluminum roasting pan; pour a cup of water in the pan. Set the turkey in the center of the grill and close the lid.
Add four or five pieces of charcoal to the grill every 30 minutes, and baste the turkey with its juices. Cover the wing tips with aluminum foil after they brown, about 30 to 40 minutes.
Grill the turkey for 12 to 14 minutes per pound; 12 minutes during warm weather and 14 minutes during cool weather. Check the color of the turkey every 45 minutes. If the turkey starts to darken too much for your liking, cover it loosely with aluminum foil.
Check the internal temperature of the thickest portion of thigh meat after 2 1/2 hours. It should measure 155 degrees Fahrenheit. Transfer the turkey to a carving board or serving tray when it's done.
Cover the turkey loosely with aluminum foil and let it rest for 15 minutes before carving it.
Brine the turkey in two turkey-roasting bags if you don't have a container large enough. Place the turkey by itself in the refrigerator's crisper drawer to brine. Oven bags sometimes leak, and you can't have liquid from the bag contaminating other food.
Soak a few cups of apple or cherry wood chips in water and toss them on the coals throughout grilling to incorporate smoke in the turkey.
The United States Department of Agriculture recommends against rinsing raw poultry. If you do chose to rinse your turkey before you brine it, use a light stream of water so it won't splatter and contaminate the surrounding area, and clean the sink thoroughly when you're done.