It is only possible to guess at google's algorithm, it is their trade secret and if they let people know it then competitors would be able use it. So it is only possible to guess what it is, it is a mixture of on site and off site facts, with backlinks and quality content being the most important.
You mention that you're interested in optimizing your on page factors... Many top SEO experts estimate that about 20% of a page's ranking ability lie in its on-page factors, where as about 80% is in its off-page factors.
The way that many of the experts learn about the Google Algorithm is by developing "test beds" of hundreds of web sites, where they constantly test their theories about what the current version of the algorithm is up to.
So short of developing such test beds yourself, you could either learn from one of these experts directly or study the free materials out and work on your own sites, until you get a "feel" for what the algorithm is going.