Skipping auto approval on Comments

By default, comments must be approved by the admin before they can be displayed.

Your comment has been queued for review by site administrators
This is what anonymous users will see when the post a comment

If you wish to avoid the message, Your comment has been queued for review by site administrators and will be published after approval, you will need to change some permissions.

Before you change the permissions so anonymous comments are not review.  We suggest you look at our CAPTCHA series (CAPTCHA and CAPTCHA - Advanced).  This will help prevent spam from flooding your comments.

Go to the people configuration and click the permissions tab (admin/people/permissions).  Under comment grouping you will see a permission for Skip Comment Approval

This is the permission to by pass comment approval.

Click the first check box, which is for anonymous users.  Click the save permissions button at the bottom of the page.