Google Webmaster Central is constantly updating and unveiling new tools for web owners. Depending on your level of expertise the features provide significant insight about your website.
For updated guidelines provide the latest best practices for web site optimization. In particular, focus on the aspects of mobile responsiveness which is quickly becoming crucial to any web presence. How far you go with these guidelines depends on your capacity and time to implement changes. This is why you may want to hire an SEO to help. The guideline offers some tips to help find a reputable consultant.
We use the Google page speed tools to check website health. Now there is another tool that checks if a website is delivering rich results. You can find the tool and run your website for free here.