Hi Todd,

how do I correctly setup the system to ensure access to the EasySocial elements of our site are restricted until registration has been approved by a person?

From what I see on your site, the lockdown mode was already enabled which would achieve your objective. If you want to also prevent the modules on the right side of the login page to not show for guest users, you can just set the access level of those modules to registered users only.

I would like an email sent to a person/s with the pertinent information and an "approve" button.

Do you mean that you would like new users to be approved by site admins first before their account is activated? If yes, you just need to set that in the profile type configuration and make sure this setting is enabled for the moderators in the Joomla's user setting(http://take.ms/xD2UB).