It's not hard, but you'll have to edit a lot of files. Your index.php file is your template for your front page. Go in there and find in the loop (after the "if have posts, the post" code) the meat of your post. There's the title, then below that the code calling the date and the number of comments. You should see this:
<?php comments_popup_link('No Comments', '1 Comment', '% Comments'); ?>
Just change the No Comments thing to whatever you want it to say instead, like "leave your comments here". If you don't want it to say anything about the comments just delete the entire line of code.
Now underneath the entry div class surrounded by span=tagged tags, you'll find a repeat of the exact same line of code (the part that makes that text at the bottom with the arrow by it) Only difference is it has the character code for that arrow there too. → . So just make sure you leave that if you still want an arrow, and than repeat whatever you changed the "no comments" thing to above.
Now, that's just your index page. If you want to change it throughout your site, you are going to have to do the exact same thing to your archive.php, search.php, and your single.php (for the post after you click on it, but this file only lists the number of comments under the title, so you only have to change one line of code instead of two.)
If you want to learn more about the variables you can use related to comments, visit
http://codex.wordpress.org/Template_Tags#Comment_tags