Pick only the areas of ductwork that are damaged to be removed. Once you have removed the ductwork, you can begin to attach the metal vent box.
Pull the duct with string up to the vent hole and with plastic ties attach to a stud every few feet so that it hangs tight.
Seal the new duct to the vent in place with plastic ties. Fasten securely since gravity will pull the flex pipe downward.
Clip the plastic ties at the end and use aluminum tape to seal everything tight. You will need to burnish with a plastic rib.
Hold the new vent in place with a wooden frame. Measure the hole accurately-cut the 2 by 4s, nail the frame together and then nail the frame into the vent hole.
Fill in gaps in the wall with insulated duct board. You will need to cut the board to size.
Prepare to seal the vent with mastic adhesive cement in order to prevent any air leaks. Once the cement has dried, replace the grate.