How do you start? Well everyone here gave you many options in their answers. Everything's online - Blogs, Tutorials, webinars, etc. Just stay focused on what's right for you. There are so many different levels of Digital Marketing - from being a freelance manager of facebook pages and twitter accounts to being part of teams in huge - digital marketing companies that specialize in very high-level operations like AgileOne that specialize in Predictive-Marketing and create complex algorithms or Pontis that specialize with Big-Data-Customer-Engagment. But these days basically every type of marketing is Digital. It just depends on whether you're a content person or an algorithms person.
Good Luck!
Good Luck!