Look at the wall where you want to install the dryer to determine the location for the vent. Insert a 5- to 6-inch long bit into a drill. Tap on the wall until you find location that sounds hollow. Place the bit against the inside wall of the trailer and drill through the wallboard material.
Set the drill aside and insert a drywall saw into the hole. Cut around the hole until it is large enough to see into. Aim a flashlight into the hole and ensure there are no wires or plumbing pipes behind the wall.
Pick the drill up and drill all the way to the outside of the trailer, creating a hole to help locate the area from the exterior.
Remove the drill bit and replace it with a 4 1/4-inch hole saw bit designed for cutting through metal. Walk outside the trailer and place the bit over the pilot hole you pre-drilled. Squeeze the drill trigger to cut the opening in the exterior of the trailer.
Expand the interior hole to a 4 1/2-inch diameter using the hole saw as well, then push a rigid metal vent pipe into the hole until it extends outside.
Walk back outside and pull the end of the rigid metal pipe over the back of the dryer vent housing. Slide the vent back and the pipe into the hole as far as possible and secure it to the trailer wall using the provided screws and a power drill.
Caulk around the perimeter of the vent housing with an exterior-grade silicone caulk.
Slide the dryer into place inside the trailer and cut a piece of flexible dryer tubing to the fit the distance between the wall duct and the dryer vent opening. Slide one end of the flexible pipe over the rigid metal duct in the wall and the other over the back vent on the clothes dryer.