I've been getting this question a lot recently.
1. You'd better be seriously interested in children's books. Not "I could be interested if I got a job in children's books". Interested NOW.
2. And that would mean that you're reading a lot of children's books --brand new ones-- NOW.
Wait, wait, you say. Isn't there on-the-job training? Why do I have to familiarize myself with children's books before I even know if I can have a career in them?
Because in spite of the low pay and long hours, we still have a lot of highly qualified people interested in being editors. And the highest qualification is the kind of book-industry knowledge that takes reading hundreds of books to acquire. Good sense about books is not something we can teach. Either you have it or you don't, and it will be much more apparent that you have it if you can speak intelligently about the books that are our current competition.
The times I have hired people, it's been pretty easy to cherry-pick the good ones. After tossing the badly-written cover letters, I ask the rest of them what they've been reading. People who are a good fit for the job have been reading a lot of children's books (and a lot of different kinds of children's books), and have a lot to say about them.
3. You'd better not have any fantasies about office work.
If you can't stand a lot of tedious paperwork, you don't want to work in publishing. We give our interns plenty of mind-numbing paper shuffling and form filling out to do, because if they make it to Editorial Assistant, it's only going to get worse. Eventually, it will get better... a little... and years later. In the meantime, you'd better be able to cope. I still have plenty of that sort of thing to do, and I do it as cheerfully and efficiently as I can so that I can get to editing and reviewing new manuscripts sooner.
4. Internships are a good way to get your foot in the door.
So have a look in your area for a publisher you could intern with. No, you can't be an editor remotely. If there are no publishers in your area, you'll have to move to where they are. Consider moving to New York. We're almost entirely here.
5. So is the Columbia Publishing course or other similar courses.