First of all, make sure you are logged in. You'll see the comment box whether you are logged in or not, but if you aren't logged in then you'll be asked to log in when you try to click the "say it!" button.
Commenting is simple: Just type what you like in the box and click "say it!" Comments support most BBCode, which is non-HTML markup system for text formatting. For more help on BBCode, see this page.
You can make comments anonymously on The Duck, but please don't abuse it. Admins can still identify the person who posted an anonymous comment, so using that feature to mask abuse or harassment is just going to get you into trouble.