To add a user to your ignore list, simply click on their user ID, and you will see their user profile. From there, just click on "Ignore postings from..." link and you will no longer see posts or private messages written by the user.
To review which users are on your ignore list, click on the "My Profile" link at the top of each page, and a list of ignored users will appear at the bottom of your profile page.
Note: when you add a user to your ignore list, that user will not know that you have done so.