But aren't you interested in minerals in they're natural state? Geology is about natural state jewellery is about polishing.
Unless you're preparing a sample for analysis then I guess you're talking of mounting your sample in a substrate then perhaps cutting to start the flat face then polishing on a rotating bed with increasingly finer grades and a suitable coolant. At uni we did it by hand when first doing it but later there were automated machines with sample holders rotating on a rotating abrasive bed.
There's various tests that need a mounted, flat and polished surface. However not commonly used by amateur hobbyists.
Not trying to be argumentative, but why do you need to polish. Why can't you appreciate the natural state you found them in? They're interesting enough imho.