How can a department or a professor advertise a class on MyUCLA?

This can now be done through the MyUCLA forums. Login to MyUCLA and click the Forums link in the column on the left. Click the Course Connections link and then the Post Topic button. Here you can enter your description of the course and any other relevant information you wish to post. Simply title the message and type the information in the message box then click the post message button. You even have the option of setting the expiration date of the message for as long as six weeks from the date it was posted.
Questions about this feature can be directed to the MyUCLA help desk at 310-206-4525 or myucla@college.ucla.edu.