In the WordPress dashboard under “Settings, “Discussion”. At the top of the page under default article settings you can un-check “Allow people to post comments on new articles”.
If you already have existing posts on your blog that you want to turn off comments for, under “Other comments settings” check “automatically close comments on articles older than 14 days” also change 14 to 1 day and save your settings at the bottom of the page. That should turn off comments on new and existing posts. If you have any existing comments on posts, you will still see them. No new comments will be allowed.