Turn the stove off and wait until all of the pellets are cold and the entire system cools off. The exterior vent pipe heats up, along with the rest of the stove, and can burn you.
Put on safety glasses, work gloves and a dust mask, before beginning the cleaning process, to avoid exposure to soot particles and other airborne debris. Close the interior doors of the pellet stove and walk outside to the location of the vent pipe.
Examine the hooded vent at the end of the pipe to determine how it attaches to the straight pipe behind it. If you see silver aluminum tape, pull it off with your fingers. If you see a bead of caulk, cut along the center of the caulk with the blade of a utility knife.
Grasp the vent hood and pull it straight out to detach it. Peer inside the cap to see if it is black with soot. If there is soot, scrub the interior of the cap with a stiff-bristled nylon brush then set the cap aside.
Insert a 3-inch flue pipe brush with a flexible rod into the straight pipe in the wall. Push the brush in with the rod portion until you feel resistance and cannot push it any further. Grasp the rod and use a push-and-pull motion to clean the inside of the pipe.
Pull the brush all the way out of the pipe. Insert the hose of a vacuum cleaner into the vent pipe and turn it on to remove all visible soot or loose debris from the opening.
Slide the hood vent cap back onto the end of the straight vent pipe and apply two layers of aluminum tape around the joints. You can also seal the joint with a bead of high-temperature RTV silicone caulk.