I would suggest looking into transitioning from graphic design into "Front End Web Development", which in a nutshell is what they call translating visual designs into the actual website that people see and interact with. It is empowering to be able to build what you design. I'd start with learning HTML5, sass & css, javascript, php and ruby/rails. Smashing Magazine has some decent tutorials, also begin reading/subscribing to some newsletters like the responsive design newsletter. HTML and sass/css is pretty easy and isn't really coding, but they are "gateway drugs" into javascript/php and learning web frameworks. I would look into learning how to "theme" websites for CMS (content management systems) like Wordpress (beginner) and Drupal (tricky), and perhaps magento for ecommerce. Javascript, php and rails will be the hard part as it will require a completely different mental mindset from what you're used to working as a designer. There are tons of free tutorials online, but paid online classes are hit and miss, if Udemy is every having a $10 sale that's not bad for grabbing some cheap classes (be warned not all the classes are good but for $10 you can't go wrong when it comes to getting a general introduction to a topic). Lynda.com can be a bit general.
It will be challenging but don't give up. The hardest thing to deal with in being self-taught in programming is documentation, it's usually written in "developer-ese" rather than plain english making it difficult to learn from. It may seem like you will be copying/pasting code you don't fully understand at first, but it gets better over time as you understanding develops.
If you happen to be female, I'd recommend joining up with Women Who Code and look for WWC meetups in your area, they have members who mentor newer members.