Fill a spray bottle with undiluted white distilled vinegar. Spray the entire shower door with the vinegar and let it soak for about five minutes.
Scrub the door with a cloth or non-abrasive sponge to remove any soap scum, mineral deposits and dirt. Apply more vinegar as necessary to help break up tough stains. Rinse the sponge or cloth often so you're working with a clean tool.
Rinse the glass thoroughly and then inspect it to ensure that there is no leftover residue. Once the door is perfectly clean, wipe it down with a microfiber towel until completely dry.
Apply a small amount of automotive windshield sealer to a microfiber polishing cloth. Alternatively, use automotive wax instead. Read the manufacturer's label very carefully for specific information on safe application instructions.
Spread the windshield sealer or automotive wax over the entire surface of the shower door using tight circular motions. Buff the sealer or wax into the glass until you can't see it anymore.
Allow the sealer or wax to dry for about five minutes, or as directed by the manufacturer. Spread a second coat of wax or sealer over the window using the same process. Allow the wax or sealer to dry for about 10 minutes, then buff the glass to a shine with a fresh microfiber cloth.