From this article here, I learned a few things about getting started with SEO. The author talks about making your page uniquely valuable, crawler/bot accessible, providing phenomenal UX, and Keyword Targeting. Also mentioned is making your site multi-device ready, built to be shared through social networks, and other metadata/markup (authorship, schema, and rich snippets) means.
The top considerations for google seems to be relevancy, value, and use of keywords and links.
I was a little suprised to find out how valuable social media can be in increasing your rank. But it makes sense to me that they would try to come up with an algorithm that judges how good of an experience the users are having with your site, and the social media use would therefore be a good measure since people share things they like.
I do think it is really incredible that they have evolved enough to use all these measurements to come up with a way to rank your site in order to give the searcher what they want!
How to Start Optimizing
So to me it seems the best way to start figuring out how to optimize your site would be to look through the users eyes. If you were to do a search that led you to your page, what would you want out of the experience? Is it delievering? Then use that to make some changes.
Other Resources for Getting Started with SEO