You want to create a discussion board area that is anonymous, so that people can post messages without requiring to authentication and without tracking their identities in discussion posts.
Here are steps to create an anonymous, stand alone dicussion area:
Step 1. Enable Anonymous Access on Existing Web Application
Central Administration > Application Management > Application Security > Authentication Providers
Click "Default"Anonymous Access > Check "Enable anonymous access" > Click "OK"
Note the description of the setting you are enabling: "You can enable anonymous access for sites on this server or disallow anonymous access for all sites. Enabling anonymous access allows site administrators to turn anonymous access on. Disabling anonymous access blocks anonymous users in the web.config file for this zone."
Tom Daddario adds "Make sure your intended Web Application is selected before modifying any configuration settings."
Step 2. Create a site collection
Central Administration > Application Management > Create Site CollectionProvide Title, URL, Template, and Site Collection Adminstrators, click "OK"
Step 3. Enable Anonymous Access on Site Collection
Site Actions > Site Settings > Advanced PermissionsPermissions for Site > Settings > Anonymous AccessAnonymous Access > Select "Entire Web site" > Click "OK"
Step 4. Create Discussion Board
Click "View All Site Content"Click "Create"Communications > Click "Discussion Board"Provide Name > click "OK
Step 5. Modify Anonymous Permissions on Discussion Boards
Discussion Board > Setting > Click "Discussion Board Settings"Click "Permissions for this Discussion Board"Actions > Click "Edit Permissions" (click "OK" to message)Settings > Click "Anonymous Access"Anonymous Access > Anonymous users can: > Select "Add Items, Edit Items, and View Items" > Click "OK"