In order to get a shiny polish, you have to start with a perfectly clean tub. If an older tub hasn't been maintained properly, you'll have to give it a good deep-cleaning and remove any stains. Use a commercial cleaning solution labeled safe for porcelain finishes, or make a solution of warm water, baking soda and ammonia, and scrub the tub with a nonabrasive sponge or rag.
If you want to polish your tub, you have to choose a product that will give it a bright shine rather than scratch it up. Products that contain harsh abrasives or highly acidic ingredients like vinegar can damage a porcelain finish. Use a product made specifically for porcelain and polish the tub with a rag. Finish the tub off by polishing with lemon oil, which will give it a shine and also help to keep future soap scum from sticking to the tub. Avoid leaving excess lemon oil on the bottom of the tub so that no one slips on it when showering or bathing.
While commercially made products will give your tub a nice shine, you may want to save money by using common household products that you already have in your cupboard. Use oven cleaner to remove stains before polishing your tub, though you should use oven cleaner only on white porcelain, as it can fade colored tubs. Once the stains are gone, give your tub an extra polish by wiping it down with shampoo. You can also use shampoo to polish the tub's faucets and hardware.
After polishing your tub, maintain the shine by wiping the tub down with a soft sponge or rag after each use and periodically washing with warm water and dish soap. If you find after time that polishing no longer keeps your tub looking gleaming, hire a professional to reglaze the tub, which will brighten the porcelain and give you a good-as-new shine.