When it comes to search engine optimization (SEO), choosing the right WordPress theme framework becomes critical. Genesis does a great job of doing all the right things for search engine optimization (SEO). You will want to add some kind of analytics tracking to your site so you can gain insight about who is visiting your site and how your site is being used. Typically most people use Google Analytics. Genesis provides a field on the Theme Settings page (wp_footer) to enter your analytics tracking code.
There are other great theme frameworks that are just as effective as Genesis but if you choose not to use a framework or prefer to build your own theme then you should use a plugin such as wordpress-seo by Yoast and use that to further optimize your pages and posts for SEO. The plugin has a ton of options which can be a bit overwhelming but typically the defaults are fine. The plugin will also analyze your pages and give you recommendations on how to improve your content, title and other aspects of the page to make it better for SEO. There are lots of tutorials on using the plugin and of course the author of the plugin is a great source for learning about SEO: https://yoast.com
A couple more recommendations: In addition to a Google Analytics account for your site you should also create a Google Webmaster Tools account and link it to your analytics account. And the other thing is to create a sitemap.xml file. The search engine crawlers look for that to more accurately index your site. The wordpress-seo plugin will create one for you but there are simpler plugins to get this task done such as google-sitemap-plugin.