If you've never thought about SEO, a reasonable place to start is with Google's starter guide. It'll help you understand the basic ways in which your site can influence the behaviors of the search engines.
And you'll want to learn about the various tools that are available to you to help you measure the effectiveness of your tuning.
Once you get past the basics, things get much more complex, and you can put a lot of effort into analyzing and studying your site to try to figure out whether it's complying with all the various best practices and policies.
But even if you become an expert, you can still be surprised and confused by the changes that occur as the search engines continually adjust their own behaviors. For people who are trying to swim in these rivers, Vanessa Fox's advice seems quite sound:
If you tie construction of your site to any one perceived algorithm signal, you’re at the mercy of Google’s constant tweaks. These frequent changes are one reason Google itself downplays algorithm updates. Focus on what Google is trying to accomplish as it refines things (the most relevant, useful results possible for searchers) and you’ll generally avoid too much turbulence in your organic search traffic.
Well put, Ms Fox!