Polishing a Micro Seiki RT 3000G Gunmetal platter

Metal polish (Brasso, Flitz etc) and a soft cloth and some elbow grease will do the job. If you're feeling lazy you could lightly use a Dremel with a buffing wheel.

I've never polished a platter, but I do use such polishes, jeweller's pastes and a Dremel to restore straight razors.

@carlsbad2 is right on.  Stopping at 3k will probably give it a very nice finish, but if you want it even shinier, I'd end with a metal polish.

Give it to a Metal Polisher and then aVustom  Automotive Sprayer to Multicoat Laquer Finish. These treatments are not expensive as a Polisher will see this as a Pin Money for cash job and the Sprayer will coat it when the Pot has Laquer in it. 

Guys, I think what @horsestuff has in mind is removing the tarnish from the metal, like polishing silver.

There are hundreds of metal polishes out there. I personally like Menzerna Polishing Cream. It is a rub on, wipe off product, a cotton or microfiber cloth will do. You could use a random orbital polisher, but on something as small as a platter elbow grease will do fine.

As Carlsbad noted, work up to finer abrasives. I like the 3m foam sanding pads for auto use.   1200, 3000, 5000.    5000 makes a lacquer finish look like glass.  3m makes sandpaper and pads for polishing / fine sanding from 1000 on up. 1200, 1500, 2000, 2500, etc