Here's what I did:

First, learn as much as you possibly can through online resources. Read the blogs. Watch the videos. A quick google search will open many doors to valuable information. If you get confused or can't find what you're looking for, then ask questions.

Then, if you're still hungry, I suggest you invest in a few books. I went with Don Norman (The Design of Everyday Things and Emotional Design) and Dan Ariely (Predictably Irrational) as a starting point. At this point, start looking at the world around you. Begin observing the way people interact with things. How you interact with things. Which points of interaction between you and a product/service do you find bother you? What could be improved? Don't limit yourself to websites and apps! Doing so is immensely narrowing your scope and potential. Begin rethinking the nature of all the relationships around you.

Once finished, I followed that up with The UX Book, The Psychology of HCI (oldie, but goodie I think you'd like) and This is Service Design Thinking, which gave me a much better overview of design and HCI thinking, processes, tools, methods and guidelines.

Get familiar with tools such as Axure and the Adobe Creative Suite. Get familiar with HTML and CSS.

Also, begin talking to people. Find products you admire and get in touch with their designers. Find design agencies or companies you'd love to work for and find a way to directly reach the people in charge. Don't be afraid to go out and create your own opportunities. Trust me, it works.

Source: Discovered UX three months ago. About to begin a paid internship at a UX/SD firm this month. I'm not enrolled in school nor have a related degree.