As others have said, the best way is to pick a field and stick with it. Not only do you become an expert and thus able to command higher rates, your per hour earnings "go up" as it were, because your research time is cut way down. When you know a field, writing about it far less time consuming, thus more bang for your buck.
I make the bulk of my money writing in the computer industry. Online help, marketing materials, training guides, grant proposals, etc. I did this for a few years as a real job before going freelance and my first clients were some people that I'd worked with. That really shortens the path to success. I also started working for a few blogs related to my hobbies and that was low paying at first and just for fun, but as people have seen my work they've asked me to do other jobs, so it's snowballed into another decent income stream.
I'll also add (not to be harsh or snarky, but just as an honest truth) that working "very part time" isn't the way to riches in this field. I know a lot of people think it's a job that can be an easy, quick thing they can do between other commitments, but if you want the serious money and the high paying clients, it has to be more of a full-time job because you're going to have to hustle for your own clients. Any sort of "agency" is likely to be very low paying. You have to hustle for your clients and then be available to them, even for things you think are petty or pesky. They're going to want revisions and the project is going to change mid-stream. They're going to bug you for last minute, super important stuff that you'll just have to do to keep their goodwill. You can negotiate all of that as far as payment terms, but you need to do it upfront and do it yourself. Agencies keep too much of the profit for themselves.
