Understanding Canonical URLs

Need help solving potential issue in Google Indexing

[FlipFlops]

After reading the featured post on the home page this evening, I decided to try the following search with Google for my major site that has had great difficulty ranking in Google:

site:domain.com -inurl:www

When I run that I see 25,400 results, all of which are listed as "Supplemental Results". When I run a normal search of:

site:domain.com

...I see 25,100 pages. It's a PageRank 3 web site showing 60 backlinks that has been active since July 13th 2004. While the site has never done well in Google, it's never done as poorly as it has in the past few months.

I have a Google Sitemap active for this site that shows no issues, indexing problems, etc.

Would anyone here be familiar enough with this type of matter to make some sound recommendations on:

1.) How to remove the Supplemental Results
2.) Prevent this from happening in the future
3.) Provide how, if at all, this relates to "canonical urls"

I've always struggled to understand this matter, and if it is an issue with my site -- I'll have no choice but to figure it all out.