Locate a safe place on the interior wall of the basement to cut in the vent. It must be away from any plumbing or electricity and about least 2 feet above the ground outside the house.
Drill a hole through the wall from the inside at the chosen spot, using a 1/4-inch boring bit.
Use your hole saw to make a wider hole centered at the first one, cutting from outside the house.
Lay a bead of caulk over the perimeter of the back of the exterior cap from the vent kit. With the cap connected to the wall tube, slide the tube through the hole, bringing the cap to rest against the wall and sealing the caulk. Make sure the opening of the vent cap is facing down.
Secure the vent cap to the exterior wall with the provided screws, putting them through the screw holes and into the siding. Caulk around the edge of the vent cap where it meets the wall.
Return to the basement. Run a bead of caulk around the joint where the tube emerges from the wall. Connect the vent hose to the tube, using a clamping belt to hold it there. Connect the other end of the hose to the dryer.