Hi, I hope my subject was ok.

I'm very new to this, but I'm trying to display a block of content to the users who have arrived at the site but have not logged in for the center position.

These would include users who are unregistered (anonymous) and users who are registered, but not logged in yet.

How do I set this in the blocks manager? I see I can categorize which blocks are visible to me, but cannot figure out how to assign a block as visible to a set of users.

Go to system admin click on Groups then on "Anonymous Users" modify or "Registered Users" modify. For each group and for each module you can give different permissions.

There are two really useful respurces available to you as a new user- the documentation site has an administration manual and our xoops.org site has an FAQ section beginners forst steps, moudles, themes, - please take some time to get to know them.