Right click most anywhere on a web page, and select "View Page Source". The code which is behind that page will pop up, and you can then search for "keyword". you can also search for any headers, titles and descriptions, which Google also likes.

That's right. No one but Google knows exactly what the algorithm looks like (to determine a site's placement on their search results). But the factors I mentioned are largely assumed to be the major factors.

To answer your earlier questions, yes. That is essentially what they do. If you have really great content and lots of it, then people will naturally start linking to it on their own - at least eventually. But a good way to get a jump start, while you're waiting to build more content and/or waiting for folks to find it, is to comment on other blogs, forums relative to your topic. You are typically allowed to use a signature URL when doing so. But if you just hire someone to go out to any ol forum and write little meaningless responses like "Cool. Nice Post", and expect the moderators to not look down the nose at the backlink . . . I think you'll be disappointed. So, you'll actually need to contribute something meaningful to the discussion there.