General terms:
* Polish: This is the most common and versatile word.
* Shine: A simple and direct term.
* Buff: Often used for polishing with a soft cloth or machine.
* Gleam: More about the effect of being polished than the action itself, but can be used as a verb (e.g., "She gleamed the silver").
More specific terms:
* Burnish: To polish by rubbing, often to a high luster. (e.g., Burnishing metal)
* Gloss: To apply a glossy finish or to make something glossy.
* Wax: To apply wax and then polish.
* Luster: To impart luster or shine.
You could also use descriptive phrases, such as:
* Make something bright
* Make something lustrous
* Refine the surface of something
The best word to use will depend on the object being polished, the method being used, and the desired result.