Best way to clean glossy finish on speakers?

I would go for the Stein way.

But whatever you do don't gloss over their instructions. 

@ghdprentice 

Almost any cloth will have dust embedded in it and will cause micro scratches… 

How true -- I learned the hard way with my piano black Silverlines  ;o/

Cory Super High Gloss

Piano Polish

Use micro Fiber Cloth

@macg19 @mijostyn is 100% dead on, though I didn't see him mention that not all foam is alike. An inexpensive rotary buffer with a soft foam pad and Menzerna 3500 or a similar fine polish will remove swirls, and return you to a brilliant shine That said though, extreme caution around the drivers, or even hand polishing if you are having difficulty controlling the buffer is a good idea. Some are base/clear coating these days, which is a HARD finish comparatively, and most are probably still using lacquer, both have been used for automotive finishes, though clear lacquer hasn't it has identical qualities otherwise to lacquer paint. Therefore automotive polish is fine. Using things like ceramic or graphene coatings can be problematic as the better ones leave your finish unbelievable slick. IOW, easily dropped. Build up  of product can be an issue as well. If I was unsure whether the finish was a softer lacquer or a harder clear coat, I'd avoid using something that might be difficult, meaning more Menzerna 3500, to remove, but that's just me. A wax or coating should add brilliance, but the Menzerna 3500 may meet all your goals.

Interesting comment about cleaning drivers cones above.

Never thought to clean them, exactly how does one go about doing that? Maybe a light dusting from a swiffer?

Because people are around and so forth I keep the covers on and they look fine.