I have no idea what I'm doing

Linux is free and can run on really old computers. buy a used/cheap computer from Craigslist and download a distro and install.

There are tons of tutorials online that can get you started.

Once you get some experience, apply for a job.

My advice would be to start small. Don't quit your day job but spend some time learning more and if you feel you are ready, try getting some one off / part time gigs to apply your knowledge in a real world setting if possible. If you can afford to offer your part time efforts for free, I'd recommend volunteering to open source projects.[1] These days most popular oss projects have no trouble finding development contributions but sysadmin / infrastructure help is hard to find. Once you have done some real world work and made contacts, switching carreers should not be hard. Hang in there and keep working at what you feel you should do. I personally know a number of people who have switched carreers successfully. Don't despair.

[1] For instance: https://fedoraproject.org/wiki/Infrastructure

I'd recommend Ubuntu -- especially if you're just starting out.

Learn how to be a Linux user first. Are you using Linux right now? If not, either install Linux on your computer, or get another computer you can install Linux on, and start using that as your main computer. immersion is a great way to learn.

My suggestion is to stop for a second thinking about the fact that you are broke. It's the easiest problem to solve (unless you need 2 billion dollars).

In my opinion the first thing you need is a clear understanding of what your goal is. Why do you want to be a linux admin? What do you like about it? What makes you say, "I want to spend my life configuring linux systems"?

If answering these questions requires more than 1 minute of your time, you are probably on the wrong direction.

Whatever you decide to do this is my advise. First, use internet. There are amazing tutorials out there for anything you want to learn. Find something that you enjoy and that makes you feel good. Experiment and "taste", the more you explore the easier will be for you to understand what you want.

Keep your job or find another job to cover your expenses. This means you have to work hard because probably you will have to study at night. I've been there, it's tough but at the same time you'll feel alive, I promise.

Learn and practice! This is specially important in computer science. Build something then try to find a way to break it. Once you broke it, build it again!

Go to meetups for people in the same field you choose. You'll learn a lot. You'll be able to start networking but mostly, you'll be able to measure your preparation and this will tell you when is time to start searching for a job.

Searching for a job won't be easy with no academic preparation. Start from the bottom and don't think about salary. For you is much more important to get hired than a good salary. Remember, you need to get hired once to be in the game!

I hired a PHP developer with a similar story as yours few years ago. I took extra steps to understand his preparation but at the end I couldn't ignore the effort and the commitment that this guy put into his preparation. Today he is a valuable component of my team and he makes me very proud of what he has accomplished.

Hope this will help!