WordPress MU

Hello,

On my web page,
http://eastcoasttechwriter.ca/wordpress/

On the right side below my graphic, I have a link that
says "Login", but this isn't working for me.

I need the link to display "Hello some person" when the user
is logged in and display a "logout" link as well".

How do I do this?

Are you sure you're using the right login tag? because when logged in, it shows logout by default.