First, you need to add that person's username to your Protected List:

How do I add someone to my Protected List:
http://help.xanga.com/howdoiaddsomeonetopplist.htm

Once you've add the usernames you want to your Protected List, you can start protecting your posts using the Weblog Editor:

How do I protect a new weblog post?
http://help.xanga.com/protectnewweblogpost.htm