Your private blog viewers will need to opt in to follow your blog by email from their account.

First, they can follow your blog in Reader by clicking the Follow button in the gray toolbar:

http://en.support.wordpress.com/following/#how-to-follow-new-blogs

To receive email notifications of new posts, they'll need to go to Reader, then click Edit List next to Blogs I Follow.

Lastly, they'll need to change the "Get new posts by email" drop down to an option aside from Never.

You can see more details and a screenshot of that here:

http://en.support.wordpress.com/following/#manage-email-and-im-settings-for-specific-blogs

How often are the auto emails sent?

It depends on the user's email delivery settings (located in Reader), which you can see more information about here:

http://en.support.wordpress.com/following/#change-your-email-settings

I hope this helps! Let me know if you have any other questions.