The most recent followers of a specific account will appear first in:
http://apiwiki.twitter.com/Twitter-REST-API-Method%3A-statuses%C2%A0followers
You can check that method periodical and page through until you start
running into users you already know are following the specific user.
Abraham
I've been asked to produce an automated response to new followers and I'm
scratching my head over how to go about handling this. I have the login to
the accounts in question, we're not fancy enough to have Oauth, and I may or
may not have access to the email account behind the given Twitter ID.