Why do we need to clean it? A build-up of dust can harbor allergens; yes, even if you live or work in steel buildings. When you're dealing with vents and radiators, the dust is propelled into the room. The excessive dust can make your heating system work harder and will cost you more money to maintain.
To clean it, turn off the heat. Run the crevice tool of the vacuum over the floor and baseboard vents. For ceiling vents, spread a sheet below and wear a hat or cap to shield your hair or eyes.
Remove the vent covers and wash it with dish soap. Use a small sponge paintbrush to get into the slats. Use only hot water if you want to soak the vent covers - take note that the paint might chip off if you soak it too long.
Clean inside the vent ducts with the crevice tool or a duster.
For radiators, dust between the radiator fins with a bottle brush. Do not use water to clean it since it will rust.