Loosen the clamp that attaches the vent to the dryer and slide the vent off.
Grab your flashlight, and take a look at the vent pipe inside the dryer. Make sure there isn't anything stuck in it, like clothes or a washrag.
Using a Shop-Vac or vacuum with a small attachment, clean out the lint from the internal dryer vent and all throughout the pipe that attaches to it. Most lint collects at the ends, but you may want to use the coat hanger to reach the middle and dislodge any remaining lint.
Disassemble all of the pieces of pipe that lead to the outside and give them a good vacuuming. And finally, take off the external dryer vent -- the one attached to the outside of your house -- and clean it out thoroughly. Ideally, your vent system is a straight shot from your dryer to the outside, but some setups call for vents to have bends, kind of like plumbing, so this will require a little extra elbow grease.