Use your variable speed drill and a Philips head drill bit to remove the screws securing the vent hood to the exterior side of your home. In most cases the vent pipe is attached to the vent hood. Cut any caulking around the vent hood with your box knife.
Remove the clamp that is holding the vent pipe to the exhaust vent on the back of your dryer. Use your flat tip screwdriver to loosen the hose clamp screw if that is the type of hose clamp that you have. Some hose clamps do not have set screws; you simply squeeze the ends of the clamp to slide it off of the hose. Remove the second hose clamp off of the opposite end of your dryer hose.
Loosen the clamp screw on the clamp connected to the metal elbow off of the dryer vent pipe. The vent pipe extends part way out of the wall and the elbow will be attached to the vent pipe if your dryer vent has one. Elbows are used to route the vent pipe to the dryer.
Grasp the vent hood on the exterior side of your house and pull out. The vent hood and the metal ductwork will slide out. Vent hoods are purchased with metal ductwork already attached. If it is not long enough you must attach enough ductwork to reach through the wall to the interior side. Use your tape measure to find the length of the ductwork.
Use tin snips to cut an extra length of galvanized steel duct if necessary to reach through your wall. Slide the duct onto the existing ductwork attached to the vent hood; snap the sides together and use your foil duct tape to seal the two sections together. Wrap the tape around the seams at least three times.
Slide the ductwork through the exterior wall until the vent hood is flush with the exterior wall. Insert the screws into the existing screw holes and tighter with your drill. Caulk between the vent hood and your house.
Attach an elbow if necessary to the end of the ductwork extending out of your wall. Use a clamp to secure the elbow to the vent pipe. Attach one end of your dryer vent pipe or hose to the elbow or vent pipe and secure it with a hose clamp. Attach the opposite end to the dryer vent pipe and secure with a hose clamp.