My question is this: I have some stainless pieces of trim that I can polish and make shine but how do you get the
"fine scratches" out of it.
To answer your question directly, you need to sand it with sand paper that's coarse enough to remove the scratches without making deeper (more coarse) scratches, then use finer and finer grits up to 2000. Then polish.
You might end up polishing it a few times to see your final results only to see that you have missed some scratches and need to redo it once again.
