As I said, feedburner.google.com . Did you visit that site ?
-Create an account
-Add your feed usually site.com/feed/ or /feed/rss or /feed/atom/
-Get a widget from them with a subscription form
-In your WordPress go to Appearance, Widgets, Add new text widget and in the text box paste the code you got from feedburner.
-Voila, users will type there e-mail address and they will get an e-mail message every time you add a new post.