MailChimp is popular email marketing service choice 
You can use MailChimp for newsletters, lead nurturing, automated emails and letting people subscribe to your blog.
NOTE: Before you watch the video below, please go into mailchimp, create a list, and just put one email address in that list (it could even be an alternative address of yours, different from the one attached to your mailchimp account)
Here’s how to create a list in mailchimp http://kb.mailchimp.com/lists/growth/create-a-new-list