Set the stove or appliance in its intended location on a hearth pad or noncombustible flooring.
Connect stovepipe sections to the back of the stove and secure them as directed. If a flue collar is on the top of the stove, you will probably need a 90 degree elbow joint to direct the piping through the wall. Otherwise, connect horizontal sections and mark the area where they will penetrate the wall. Maintain a safe clearance of 18 inches between the stove pipe and the ceiling and other combustibles.
Cut an opening in the wall that is large enough for the wall thimble to pass through. To do this, drill a starter hole and cut the hole from the inside using a jigsaw or another power cutting tool. From the outside, continue cutting the hole until it is complete.
Install a wall thimble in the holes you cut, based on the manufacturer's instructions. The wall thimble serves as an insulating sleeve for the stovepipe to pass through. Adjust the sleeve based on the thickness of your wall. Secure the wall covers in place with appropriate screws. Apply silicon caulking around the perimeter where the thimble penetrates the wall.
Install the tee support, the tee and the cleanout bracket into the wall thimble. Secure with screws or as directed. This hardware forms the base of the chimney and collects creosote that drips from the chimney flue.
Attach chimney sections and secure them to the tee bracket, maintaining a clearance of 2 inches from the wall. Mount the bracket to the wall, with wall straps, every 8 feet. Extend the chimney so it reaches at least 3 feet above the nearby roof line.
Place a chimney cap on top of the chimney; secure it with sheet metal screws or silicone caulking.