Everybody says that a major thing to help with game performance is the hiding of polygons that are not currently seen on screen. How is this accomplished?

I usually hide mine under the carpet, or behind the wardrobe.

Seriously though, there are several ways to do this and most combine together. Have a look at the development resources on this site and you''ll find loads. Look at things like Quadtrees, Octrees, Culling, PVS, BSP, Portals and you should get some info.