Before polishing, clean the solder (see cleaning tips) and apply the patina, if any.
Use a good quality furniture polish or wax. Shake the bottle well if it is a liquid, then apply liberally to a soft cloth, or good quality paper towel, rubbing all over solder. If you have a glass with a deep texture, try to avoid this all over process, as it can be hard sometimes to remove all of the polish afterwards, and it is noticeable when it dries. Alternatively, mask off the glass from the solder.
Immediately after applying the polish, take a clean, dry soft cloth or new paper towel, and begin to gently rub the solder seams. If you are using paper towels, you will need a lot of them, as they tear up quickly. When both sides have been polished, check for any missed spots, especially along the edges of your solder seams. Also check for polish residue in tight corners and along the edge of the solder. An old toothbrush often works to remove it. If you need stiffer bristles, make sure you keep this new toothbrush separate from all the others in the house.