Here are some useful tools from Google that will help you to improve your website.
First start with analyzing your website traffic with Google Analytics.
Google Analytics
Make your website faster with Google PageSpeed Insights. This tools gives you a detailed report about your website with recommendations about how to increase your website performance.
PageSpeed Insights
Investigate your site with Google Keyword.
Google Keyword
What is your Pagerank?
Google Pagerank
Investigate search terms with Google Trends
Google Trends