Remove the door knob from door by removing the screws on the knob plate (the part that touches the door). Pull the knob on each side away from the door. Removing the knob will ensure that the door paint is not damaged.
Wearing gloves, polish the knob by using a small amount of brass-specific polish on a clean rag. Rub it in a circular motion until the tarnish has been removed. This may take some time. It depends on the amount of tarnish on the brass. You want it to retain its antique look, yet not maintain any rust or dirt.
Pay attention to the details. Antique (and faux antique) brass door knobs often have precise detailing. Use a q-tip to polish any areas that a rag may have missed.
Once all of the tarnish has been removed, wipe the knob down with a clean rag until it is free of any polish residue. It should look as antique as it did the day of purchase, not marred by contemporary use.
Reinstall knob by pushing pieces together. Reinstalling the screws through the plate and into the door.
Wipe fake antique brass door knobs down daily to keep grime and build-up away from them.