First, to see how email subscriptions work, why don't you go ahead and subscribe to this blog. All you have to do is click this link and fill in your email address:
Then, go to your email inbox and click on the verification link. Presto! You're now on the mailing list. Each day that there's a new post on this blog, you'll receive an email that contains all of the new posts from the last 24 hours. You'll have piece of mind that you aren't missing any of the exciting educational goodness taking place on the Arizona K-12 Center's blog!
Next, let's discover how you add a link to your blog like the one above. It doesn't matter what software or service you use for your blog; Edublogs.org, Blogger.com, Tumblr.com, etc. will all work. You will need to select the URL/web address of your blog and copy it. For example, this blog's URL is http://azk12.org/blog.
Go to Feedburner.com and click Register. Complete the form to set up your free account. If you already have a Google account, then you will use that to register.
Click the Get Started link.
Paste your blog's URL into the box. Click your way through the setup process.
Click the Publicize tab from your feed's menu.
Click Email subscriptions along the left side of the page.
Click the Activate button.
Almost done!
Feedburner provides code for a web widget to embed on your site.
However, you probably just want the URL to send your readers to instead of a web widget. That URL is hidden in the code. Below I've highlighted the URL you'll want to copy from the code Feedburner gave me. Yours will be similar but will end with something other than azk12-tech.
<form style="border:1px solid #ccc;padding:3px;text-align:center;" action="http://feedburner.google.com/fb/a/mailverify" method="post" target="popupwindow" onsubmit="window.open('http://feedburner.google.com/fb/a/mailverify?uri=azk12-tech', 'popupwindow', 'scrollbars=yes,width=550,height=520');return true"><p>Enter your email address:</p><p><input type="text" style="width:140px" name="email"/></p><input type="hidden" value="azk12-tech" name="uri"/><input type="hidden" name="loc" value="en_US"/><input type="submit" value="Subscribe" /><p>Delivered by <a href="http://feedburner.google.com" target="_blank">FeedBurner</a></p></form>
Link to the URL on your blog. It's best to place it in a sidebar so that the link shows on every page of your blog. Since this is like any other URL/web address, you can put it on your school website or send it through email. If you want to include the link in a printed newsletter, I suggest first shrinking the URL using TinyURL.com.
Now that you're all set up, you don't have to do anything more. Feedburner checks your blog everyday and automatically sends out an email to all subscribers if there are new posts.
You can log into your Feedburner account to track your number of email subscribers. Additionally, Feedburner allows you to customize the emails with a logo and other settings. With some more setup, Feedburner can track all of your subscribers, not just those subscribing through email. Finally, you might be interested to know that Feedburner works with podcasts too!
What if you could automatically send an email to your readers when you update your blog? You can with Google's free 
feedburner.com/fb/a/emailverifySubmit?feedId=2540219&loc=en_US