Welcome to anonymous_qs! Questions are posted via the box on the main community page, and are then submitted to LJ for moderation.
If approved, the question will appear in the community (posted by anonybot), and people can comment on it as usual. IP logging is turned off and anonymous commenting is enabled to allow you to post freely without fear of monitoring.
A couple of rules:
1. Try to make it interesting, or relevant, or something. The question "what should I eat for lunch?" doesn't need to be answered anonymously, and won't make it through the moderation process.
2. Don't call out other people by name, in comments or in posts. The only person who is entitled to ask a "What do you think of <lj user="whoever">?" is them. Again, if you're starting trouble, you won't make it through the moderation queue / your comment will be deleted.
3. Racial slurs and other disgusting comments will not be tolerated. See this post.
Otherwise, have fun! Since you don't need to be a member of the community to post a new entry or comment, there's no need to even join the community in order to take part. Nobody need ever know you were here.
This is, in effect, a 100% anonymous question/answer community.