What do I do?
1. Find and install the Mollom module (http://drupal.org/project/mollom). It is currently the best spam protection module for Drupal 7; there are others (http://drupal.org/project/modules?filters=tid%3A7266) but none with the flexibility and reliability of Mollom.
2. Register an account with Mollom, get a key.
3. Configure Mollom on your site by adding the key.
4. Enable anonymous comments on your site. The settings are under Admininstration > People > Permissions (i.e. yoursite/admin/people/permissions):
5. Enable comments for one of your content types. You do it via going to Admininstration > Structure > Content Types and clicking the Edit link for your content type of choice. For example, to enable comments for your content type Basic Page, the path is yoursite/admin/structure/types/manage/page. Here's a shot of that settings page with comments enabled:
6. Enable Mollom protection with CAPTCHAs for the comments on that content type.
If you have done everything right, your comment form will look like the screenshot below: