Hello
This particular example was created with an embed form frim MailChimp (
http://mailchimp.com/). Once you have an account and logged in navigate to Lists -> Signup Forms to obtain the markup for your form. This markup can then be added to a custom module (Extensions -> Modules -> New -> Custom) using the CodeMirror editor or you can edit the current newsletter module ('Signup to our Newsletter').
There is a number of alternatives to MailChimp and you will find the same process will work regardless of the provider you decide to use,
CiarĂ¡n