Put on your rubber gloves and remove the cover from the drain by unscrewing it with the screwdriver.
Insert the pipe-cleaning brush into the drain as far as it will go, then work it in and out to loosen the rust and remove any big chunks.
Pour rust cleaner over the brush and about 1/2 cup down the drain. Re-insert the brush in the drain and work it in and out for a couple minutes, then pour another 2 cups or so down the drain and allow it to soak for half an hour to an hour.
Pour 1 or 2 gallons of water through the drain to run the rust remover out of the pipe, then reconnect the cover for the drain with the screwdriver.