You could try small-circulation local magazines; you may have to approach a few before you find one willing to look at the work of a writer who doesn't have any professional experience of writing for publication.
Can you look at a variety of publications and come up with ideas for pieces that would be of interest to them? Look carefully at the structure and content of their articles. How would you research an article - how would you get the information you'd need? Do you have any hobbies - magazines for, eg. dolls house enthusiasts sometimes use stuff from people who really know the subject.
Don't be too ambitious at first and send stuff off to mainstream titles, because they will only look at stuff from people who really do know what they are doing (don't mean to be rude, but it's like any other trade, it's hard to get in without training).
Almost all freelance non-fiction writers are journalists who have trained and been employed before going freelance. Even people who have trained as journalists usually have to do unpaid work experience before they get their first job, and then have a job or several before they go freelance - it's a very competitive field. I'm not trying to put you off, just saying you have to be aware that it may well be difficult and you'll need a lot of persistence.
If you really, really want to do it, then it's worth a go but you may have to knock on a lot of doors before you get a break.