I've been thinking a lot recently at trying to do this kind of work as well. I'm just not sure where to start. I have a pretty weak network form living abroad for so long and moving around a lot.
Any advice about how to even get started doing this kind of work? What tools to study or learn? How to find work?
Don't move around all the dang time. I've lived in two places and have an incredibly strong network in both. I find people who are bouncing around 50-times-over usually lack the deep business relationships that it takes to establish trust to solve "big" problems.
As far as getting started - once you start, just never stop. Solve every dang problem you can get your hands on big or small, and continue to publish code every day.
Tools to study and learn - web web web. Also Microsoft Excel automation is an incredible need for lots of businesses. Puppeteer, and learning how to mimic what a browser can do without using a browser would be the two most useful skills I have personally. If you don't have a VERY solid background in webdev you need to get that going first, so much of what I do is reverse-engineering someone's website so I have to be very versed in the way that sites are built (all the way from ancient ones to the most modern of frameworks).
How to find work is network. Once you have the skills, you need to know people that have potential needs. I've already reached out to two people who found me through this thread and regardless of "making money", I genuinely want to help them, if even to just point them in the right direction (like yourself).
People are (*generally) awesome if you put aside your own ego, and I would be absolutely nowhere if I wasn't a sociable person. I love to learn about the world by making connections with people, and genuinely want to help them with what I can do!
Any advice about how to even get started doing this kind of work? What tools to study or learn? How to find work?