Choose a site for your grill. Select a location on concrete, not bare soil. Keep the site away from your house and overhanging structures or trees.
Lay down the charcoal tray on the ground where you plan to install the grill. Draw a line around the perimeter of the tray, but leave a 1/2-inch gap between the grill and the chalk. This chalk mark will show the outer edge of the grill. You will build your grill in a U-shape around the sides and front of the tray, leaving the access opening in the back.
Dry fit the bricks around the exterior of the chalk perimeter. Leave a 1/2-inch gap between bricks. Remove the bricks and set them in an easily accessible area.
Mix the mortar in a 5-gallon bucket according to the manufacturer's instructions.
Spread a 1/2-inch layer of mortar over the ground around the chalk perimeter. Use a trowel.
Set the first layer of bricks in the mortar. Spread the sides of the bricks adjacent to other bricks with 1/2 inch of mortar.
Spread the top of the first course of bricks with mortar, then place the next course of bricks in the mortar. After constructing each course of bricks, use the trowel or a pry bar to scrape the excess mortar from the front of the structure. Stagger the placement of the bricks in the mortar. This means that the second course of bricks will start with a half brick instead of a whole brick, and the third course will start with a whole brick. The first brick in each course should alternate between a half- and whole-sized brick. If you need to cut a brick in half, use a hammer and chisel to score a seam around the brick where you'd like to cut it. Pound the seam of the brick with the chisel until the brick breaks.
Build up your grill by six courses. On the seventh course, turn in the bricks on the sides of the grill so they're perpendicular to the other bricks. The outer edge of the side bricks should be flush with the edges of the grill, and the interior edge of the side bricks should jut into the interior of the grill. In this way, you will create a shelf to support your charcoal tray.
Build up the grill by another two courses, and on the third course, create a second shelf to support the grill. After constructing the second shelf, add two more courses of brick.
Paint the brick structure with a concrete-bonding material, then wait for it to dry, according to the manufacturer's instructions.
Mix the stucco in a bucket while you wait for the bonding agent on the grill to dry. Stucco is a mixture of sand, water and cement, but you can purchase pre-mixed bags of stucco at your local home-improvement store. Add water to the stucco according to the manufacturer's instructions.
Smear the brick with a layer of 1/4-inch stucco. Use a trowel. This layer is called the "scratch coat."
Make deep grooves in the stucco with a plasterer's rake. Allow the stucco to cure for 48 hours before moving to the next step.
Apply a second layer of stucco to the scratch coat. This layer should also be approximately 1/4-of-an-inch deep. You may make textures in the stucco as desired. Wait for the final layer to cure according to the manufacturer's instructions before painting or using the grill.