Lay an old towel or some paper down on the floor underneath the vent to catch any dust that falls during the cleaning process.
Vacuum the vent using a vacuum cleaner attachment to suck out the dust from the duct.
Run a damp rag over the vent to get any stubborn dirt out, which should stick to the rag.
Spray compressed air into the vent to dislodge any dust that's a bit deeper inside of it.
Wipe the vent down again with a dry rag to eliminate any remaining dust and remove the moisture left by the wet rag.
Remove the paper or towel and vacuum any loose dust remaining on the floor.