How can I turn off WordPress Comments?
You can turn off commenting for all future posts in Settings > Discussion. (Must be logged in as an Administrator to do this.) Uncheck the top box labeled "Allow people to post comments on new articles."
Comments added previously to posts will still display on the posts. If you want to take them off the posts, you can go to Comments, select one more comment, then use the Bulk Actions drop-down menu in the upper-left to select "Unapprove" and hit the Apply button. If you have lots of comments, you might need to repeat this depending on how many comments are displayed on this screen. This will remove the existing comments from the existing posts, but the existing posts will still have commenting enabled.
So step three, to remove the possibility of further comments on existing posts, go to Post > All Posts, and do the Bulk Actions > Edit thing on some of all of the posts, and under Comments in the Bulk Edit screen select "Do Not Allow." This will prevent comments from getting added to those posts going forward.
Here's another good resource on this, which includes a gratuitous but amusing comparison of WordPress comments to the murder of Rasputin.
None of the above will delete existing comments. You could do that using a Move to Trash bulk action in the Comments screen, but there's no need to do that once they're removed from post pages.