Put a small amount of copper cleaner on a cotton rag. Copper cleaning products are commonly a paste or thick liquid. A liquid copper cleaning product is easier to maneuver around the pipe in a small area, and is also easier to wipe off.
Wipe the rag along the copper pipe vigorously. Dirt and varnish will break down and become clean with several strokes of the copper cleaner on the rag. Apply more copper cleaner if necessary to remove stubborn dirt, varnish and discoloring.
Wipe the copper pipe with a clean rag to remove the cleaner.
Buff the pipe with a lint-free cotton rag to increase its luster.