There are basically two polishing methods used in jewelry making:
Mechanical polishing
Felt or cotton discs dipped in abrasive compounds are used to polish the surface of the metal. For difficult places to reach, (crevices, inside angles) cotton threads/strings in the same abrasive compounds are placed in the hard to reach areas and are vigorously rubbed.
Chemical polishing
This type of polishing is risky and is not appropriate for all alloys used in jewelry making.