Locate the area of the basement ceiling between floor joists where you will penetrate with the piping. Connect the stove pipe sections to the flue collar on the appliance or stove and determine where the piping will penetrate the ceiling.
Measure and mark a square in the penetration area, based on the size of the ceiling support box.
Drill a starter hole and cut the square out with a jigsaw.
Mount the ceiling support box in the square opening, according to the manufacturer's instructions. The support box serves as an insulating passage for the first floor that the pipe penetrates. From then on, you must install firestop radiation shields at each ceiling penetration.
Run chimney pipe sections to hang down through the support box. Connect the chimney to the stove piping with an adapter.
Cut holes in all additional floors to continue routing the chimney to the roof. At each floor, cut a hole based on the size of the firestop radiation shield and mount for each pipe passage as directed by the manufacturer.
Remove roof shingles at the area where the chimney will penetrate, using a pry bar. Cut a hole the size of the chimney flue in the roof, adding any necessary clearances. Many building codes require 2 inches of clearance on all sides between the flue and combustible materials.
Extend the chimney sections to reach at least 3 feet above the surrounding roof line.
Slide metal roof flashing under the shingles around the pipe. Reattach the shingles you removed with roofing nails and a hammer. Mount the storm collar to the chimney with bolts.