There are two ways to disable comments.
Disable comments for each Post or Custom Post Type
Comments are enabled in WordPress by default. You can change this default for new posts or pages you’ll publish in the future, as well as change it for posts or pages you already published.
To change the defaults for new posts or pages, go to Dashboard → Settings → Discussion and uncheck this option.
To disable comments on an existing post/page/project, open it for editing. Under the main content area, you should see a box labeled “Discussion”. Simply uncheck both boxes and save your changes.
What if you can’t see the discussion box? Then you need to click the “Screen Options” tab in the upper right corner of your screen and check the box to enable the discussion module. You still need to close the tab and navigate to the bottom of the page and uncheck “Allow Comments” in the discussion module.
Disable comments throughout the website (everywhere)
You can also use a plugin like Disable Comments to disable the comments site-wide in a single step.