If you would like to extend Cloudflare's CDN to cache more than static content by default, you can use Page Rules to extend the caching capabilities to cache more content. Page Rules can be accessed by going to the settings for the domain that you want to create a Page Rule for. Once you are on the page for Page Rules, you would then place the URL in the selector box that you want to extend caching for, such as:
http://sub.yourdomain.com (for a subdomain)
If you want to cache everything on http://www.yourdomain.com, then you would want to input the URL like http://www.yourdomain.com* (include the star) and choose "Cache Everything" in the cache option drop down selectors. The same logic would apply to any other url that you want to cache.
Important: Caching everything can cause issues with admin sections of the site and other logged in sessions. If you do not want to have caching function on these specific urls, then we recommend setting a Page Rule to exclude these *before* creating a Page Rule to cache everything.
Related: Page Rule tutorial