The best way to clean a dryer exhaust vent is by cleaning each section of the vent with a brush made specifically for the task or a long-handled brush that fits. Use the brush to loosen lint and dirt from each section, and vacuum up the lint remaining.
Cleaning the lint trap every time the dryer is used is the first step in keeping the dryer exhaust vent clean. If the dryer is not drying clothes in the normal amount of time, or if the clothing or dryer seems hotter than usual at the end of a cycle, it's probably time for a more thorough cleaning.
To clean the vent, pull out the lint trap and use a brush to pull up lint from the lint trap cavity. Vacuum the head of the brush clean, and repeat the process until no more lint comes up with the brush. Put the lint trap back in, then unplug the dryer, turn off the gas if it is a gas dryer, and disconnect the duct joint that is closest to the dryer.
Pull the dryer away from the wall and disconnect the sections of dryer duct. Clean each section in the same manner as the lint trap cavity, and clean out the exhaust discharge cap outside the house. When finished, reassemble the duct and reattach it to the dryer. Move the dryer back to its normal place, turn the gas back on if applicable and plug it in.