To achieve this to all pages you should edit
header.php file and add your code there or if you want it to display only on front page just like Call for Action section which comes with theme you can edito extras.php file.
More specifically you should look for function called
sparkling_call_for_action and add your code somewhere between the lines.
To get subscription form itself you can use plugin and service such as Mailchimp. It provides code snippet as well as shortcode that you can use inside content or template files. You can find more on plugin documentation.
Of course, you will have to style this forum to make this form blend perfectly with the rest of the theme layout but those changes are up to you.