To view applications to join your blogring, please see:

How do I see who has applied to join my blogring?
http://help.xanga.com/whohasapplied.htm

Once you've on the pending tab of your Approve Members page, you should see a list of applications to join your blogring.

Under each application will be a link labelled "Read More".  Once you read the application, you'll be able to click on the links that say "Approve" or "Disapprove".  Doing so will approve or disapprove the applicant's membership in your blogring!