I am creating a directory and have a custom post type called "listings".
I want to display a grid of "Most viewed" listings as well as "Highest rated" listings on my homepage and throughout the website.
I am really not sure how to do this.
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For most popular you can use something like https://github.com/williamsba/WordPress-Popular-Posts-with-Custom-Post-Type-Support/blob/master/wordpress-popular-posts.php
Actually there are several plugin and solutions it you check google, did you try it?
If using a plugin is a problem then try custom code, see solution here https://stackoverflow.com/a/30142214/2975536