This is a basic script, which will hide the who is online section from any user that is not logged in. After making the edits, save the file and re-upload. If you do not use subSilver, make the alteration to the index_body.tpl file of the template you do use.
OPEN templates/subSilver/index_body.tpl and FIND:
BEFORE THIS SEGMENT, ADD:
BUT, AFTER THIS SEGMENT, ADD: