I was wondering if someone could give me a detailed description of what the advanced rendering options mean and perhaps some advice on how best to use them.

Thanks!

I would like to know that info also. 
If someone could also give some hints or trick about how to eliminate the pixelization, (those little black patches of pixels that jump around every time you rerender them), that always show up in every render, it sure would be welcome. I hope postwork is not the only answer for that problem.

Render Quality modes;
http://www.pixelrobotics.com/tuts/br_render_01.htm

Advanced render Options;
http://www.bsmooth.de/BSolutions/#B5RenderOp

how to eliminate the pixelization, (those little black patches of pixels that jump around every time you rerender them), that always show up in every render-You should expand on that problem (your settings), because that should not be happening.

Here is acomparison of two renders of the same picture using the same settings. You can see the problem I'm talking about prominently in the round steps in the front of the picture.  Every time I rerender this scene the black pixelatin moves and even when I spot render the trouble areas the pixelation moves around. I will make another post with the settings used to render them. I am unfamiliar with including picture files so bear with me.

Here are the settings used in both renders.

Comparing your render settings to what I used in a high RPP rendered scene, the only thing I can see thats different is to change the "general" setting from "preview render" to "full render" and see what that does. Your RPP should be high enough to nuke most artifacts.

well, I tried the suggestion put forth and also changed the RPP upwards and there seemed to be no difference in the problem.  I thought it may be because of the combinations of the sky lighting and resolutions or one of those parameters alone so I changed each one in turn and rerendered , but unfortunately, no change. Frankly, I am at a loss to figure it out. You can see from the enclosed picture that changing the sky lighting had no effect on the problem. Aside from that or because of it, I would like to know the parameters some of you use successfully for your poly intensive scenes. Any suggestions will be greatly appreciated.

That doesn't look like an AA problem to me. How are those stairs built? Are they a single mesh or seperate meshes stacked? If they are stacked, I'd give the BSP algorithm and Aggressive optimization a try. Both of those are for use with complex scenes w/ clustered and/or overlapping objects. The 48-bit dithering might help too, because that is used for removing color banding... 'Evening skies' is the example used in the manual where it might be good to use dithering.

The attachment shows settings that I used a little while back successfully for a very complex render.

More rays for pixel and turn on the 48-bit dithering. (Gamma correction isn't necessary, and will shift the brightness.) Back in the ol' (Bryce 4) days I'd also say use the anti-aliasing, but that's not an issue with premium rendering.