Entityform uses the Rules module for its notification system. When editing an Entityform Type, you can select rules to be run upon saving an Entityform Submission under the Notifications Settings tab for the Entityform Type. Rules and Rules Components that are tagged with "entityform submission" will be shown in this list.

Installation

1. Install and enable Rules and Rules UI. Note: if Rules UI is disabled, then the Entityforms Rules will not show up.
2. Install and enable Entityforms.
3. Create an Entityform Type.
4. Click on the Notifications Settings tab.
5. Configure the notification settings as desired.

Note: there are also settings at Configuration » Content authoring » Entityform settings. (I assume these are for defaults that will be used when creating a new Entityform Type, but this needs confirmation from the module maintainer.)

Entityforms Rules

There two default Rules that come with the module:

1. Email Entityform Submitter: Sends an email to the submitter.

Here is a simple way to leverage the power of rules, views bulk operations, private message, private message growl and shoutbox to create a simple chat solution for your site. Site runs on shared server with limited resources and php 5.2
Please note that after one month of using this solution I found envolve chat module which is what I am using on my site now as it reduces the burden on the system.
My Requirements:

1. One single public chat on the site which auto updates
2. Notifications to active logged in users on the site only
3. Per user ability to opt out from the notifications messages

Step 1: Module Requirements (D7 versions):

1. Private message
2. Views
3. Views Bulk Operations
4. Private Message growl
5. Shoutbox