Unplug your dryer, and pull it out from the wall.
With your screwdriver, loosen the screw on the metal tension belt that is holding the exhaust hose to the back of the dryer. Take off the hose, making sure to leave the tension belt on the tube.
Reach into the exhaust hole in the dryer and manually remove any lint you find. Do the same for the open end of the hose, reaching into it as far as you can and removing lint.
Disconnect the hose from the exterior wall by unscrewing the screws holding it to the exterior vent. Manually clean out the opening of the hose as before. Then re-attach the hose to both the wall and the dryer.
Outside the house, climb your ladder to the exterior vent. Remove it by taking out the screws holding it. Bring it down the ladder and use your garden hose to spray all lint off of it. Set it in the sun to dry.
While the vent is drying, going back in the house, plug in your dryer, and run it on the fluff setting (no heat). Shake the exhaust hose around a few times as the dryer is working. Without the vent on the outside of the house, this will expel any addition lint from the system. Let it run for a few minutes, then turn it off, go back outside and screw the vent back into place.