I’m no expert, but I also don’t consider myself a newbie.
From what I understand about wordpress, it would be impossible for anonymous users to post (we’re talking about an actual post here, not comments on a post), because first, they need to get in to the dashboard.
It is possible, however, to create a new user yourself that is named “Anonymous” with a password that is made public on your site (Tell them to click on “Log in” and use username “Anonymous” and password “pass”). Then, while logged in as an administrator, you can change the role of “Anonymous” to Contributor (under the users tab on the site admin page).
That being said, I would have to recommend that you not use wordpress in this way. There are absolutely no spam checks on new posts, and I think your site could go downhill quickly as soon as a spambot or two found out about it.