Turn the furnace off at the thermostat to stop the airflow while you're cleaning the heat ducts. Vacuum or sweep the area immediately around the register so debris doesn't fall into the air duct when you remove the cover.
Put on a pair of gloves to protect your hands. Remove the screws attaching the cover and pull it off the wall register or lift it up from the floor register.
Reach carefully inside the duct with a brush and a rag and wipe down any accumulation of dust, dirt and debris off of the walls.
Put the crevice tool on the vacuum cleaner hose. Turn the vacuum cleaner on. Reach in as far as you can and clean the dust, dirt and debris out of the nooks and crannies.
Change the end of the hose to the brush attachment. Reach in again and sweep the heat duct to remove as much debris as you can.
Sweep off the top side and the under side of the register cover. Spray a rag with all-purpose cleaner and wipe off any grime, if need be. Wipe the cover dry, then reinstall it over the register with the screws.
Turn the furnace back on.