Ask your assistant to stand outside to watch the dryer vent, and turn on the dryer from the inside to heat the vent and scare the birds out. Go outside and wait. If the birds don't come out of the vent, that means they've already gone on a food run and they'll return within a half hour. Once you're certain that the birds are out, proceed to step 2.
Stretch a wire coat hanger, and make a hook on the end of it.
Position a ladder under the dryer vent and climb it. Stick the hanger into the vent, and pull back when you feel the bird's nest until you can use your hand to take it out. Wear gloves so that you don't come into contact with any babies or excrement because there may be a risk of avian flu or other diseases.
Push the hanger farther into the vent to pull out as much of the nest as possible.
Go in the house, and move the dryer away from the wall and take the aluminum dryer hose off the inner vent.
Push a long garden hose up through the vent until it comes through the outer vent. This will ensure that you've gotten the entire nest out of the vent.
Install the vent guard to ensure that the birds can't move back into the vent.