Mesquite wood smokes cleaner, reaches a higher temperature and burns longer than other barbecuing woods, and requires only a few minor tweaks in the standard starting procedure. Mesquite produces a stronger flavor than other hardwoods, so it works best with meat, but you can use it for delicate items if you use less of it. You have the choice between mesquite chips and chunks, and both have their merits. Mesquite chips smoke faster but need replaced more often, and are great for burgers and steaks. Chunks burn slower, making them better suited to smoking and foods that need a lot of time.
Soak mesquite wood chips in water for about an hour before you start. If you're using chunks, don't soak them.
Empty the ash from the charcoal tray and clean the grate with a grill brush. Carbonized fat and proteins diminish the cleanness of mesquite smoke. Open the vent on the bottom of the grill.
Add enough natural lump charcoal to the chimney starter to cover the charcoal tray with two layers if you're grilling with high heat, and enough to form a single layer if you're smoking. The amount of charcoal you need depends on the size of the grill. Place a piece of newspaper in the bottom chamber and light it.
Let the charcoal burn until you see a glowing red mass in the center of it, and then empty it in the tray. Spread the charcoal out evenly in the tray, and then add enough unlit pieces in the center to form a slight mound. If you're barbecuing delicate items like fish or food that takes more than a few minutes to cook, such as a whole chicken, push the charcoal to one side of the tray for an indirect heat source.
Scatter the mesquite wood chunks over the charcoal, spacing each piece about 3 to 4 inches apart if you're grilling. Space the wood chunks about 2 inches apart if you're smoking. The exact amount of mesquite you need varies depending on the size of the grill. If you have mesquite wood chips, scatter an even layer over the charcoal.
Allow about 10 minutes for mesquite wood chunks to smoke, and then add the food. Mesquite chips start smoking a couple minutes after you add them.
Lay the food on the grill. If you're grilling quick cooking foods, such as steaks, fish or burgers, you don't have to worry about replenishing the mesquite. If you're using mesquite chips, replenish them every 15 to 20 minutes. If you're smoking food or grilling something that takes more than one hour, add a fresh layer of charcoal about once an hour or when the heat starts to drop, and spread another layer of mesquite chunks over it.