I'm not sure if this is the correct way to do it, but it works. In the Dashboard>Design>Theme Editor files, I commented out all the references that were calling comments, like this:
<!-- <a href="<?php comments_link(); ?>" class="commentsLink"><?php comments_number('No comments','1 comment','% comments'); ?></a> -->
Everything between <!-- and --> is what was there originally. I could have just erased it all, but this way I can add comments back later if I want. Go through each of the files (single.php, posts.php, etc) and do this for each one.