When I share a status update or other posting (video, photo, blog, discussion, reply etc), nothing appears or happens to the Latest Activity feed on my page or on the home page.  How do I fix this?

Click on Privacy Settings from the My Page menu.  Then review the Latest Activity toggles to enable the types of postings you would like to appear in the feed when you post them.  See screenshot below for reference:

If you have your "My Page" visibility set to "Friends Only", that will also cause your status updates to only appear on your page, but not the main latest activity feed on the home page.  Changing visibility to Members Only resolves this.  These settings are also under Privacy.