You need the reCAPTCHA keys here and/or the MailHide keys here
If you plan on using MailHide, you will need to have the mcrypt PHP module loaded (Most servers do)
If you turn on XHTML 1.0 Compliance you and your users will need to have Javascript enabled to see and complete the reCAPTCHA form
Your theme must have a do_action('comment_form', $post->ID); call right before the end of your form (Right before the closing form tag). Most themes do.