It's very simple. Go to your Admin dashboard, click the light switch icon that will bring you to the Wiki Features options. Scroll down until you see the option "Require all contributors to login" or something like that; just click the gray button below, making this will prevent all anons to contribute to the wikia.
I guess you're going to do this on Terrible TV shows wikia, right? Maybe some troublesome anons are pestering that wikia just like thy did here? Anyway, the Wiki Features page offers a lot of options, like switching off the chat, if no one uses it.