Buy lean cuts of meat. They will create less drippings and therefore less smoke. For beef choose at least 90% lean, and opt for white meat over dark meat poultry.
Clean your grill. Old chemicals may transfer from the grill to your food.
Choosing smaller cuts of meat will limit exposure time on the grill and reduce risk of carcinogens. Kebabs are great for this. You can even pre-cook meats and vegetables in the oven, remove some of the drippings and finish them off on the grill.
Trim excess fat and remove skin from meat, this will cut down on the drippings and smoke.
Avoid flames near your food by putting meat or veggies on a sheet of foil. For meat, poke holes in the bottom to let drippings fall. The foil will protect food from smoke and cut back on high flame flares.
Flip burgers and meats often to make sure they are not charring. Discard charred meats or vegetables.
Grill tofu or vegetables that do not have proteins that can transform into harmful chemicals. Just make sure they do not char.
Eat grilled foods in moderation. Even following all of these safety tips, grilled food will still have carcinogens.