Freelancing is similar in some ways to blogging. For one thing, you get to work from your own home most of the time. But there are a few important distinctions. With freelancing you're generally selling your writing to another publication as opposed to just putting it on your blog (although some bloggers do both.) Many freelance writing positions cover specialized topics for online publications and may require expert knowledge of the subject. Of course, seasoned journalists, who may not have specialist knowledge, but are good at interviewing and researching to get that knowledge, also have careers freelancing for various newspapers and magazines. You could specialize in writing about food, health care, business or just be an all-rounder. However, it helps you get more work if you can point to expertise or experience in a particular niche.
To get started, you may have to write for free. Many small websites are looking for free writing help. Once you get some clips, you can show them to someone who's offering paid work. Check general job sites like Indeed.com or the "About" section of your favorite publication to see if they are hiring and what the requirements are.
You might also consider self-publishing your original work rather than working on contract-driven tasks. Self-publishing offers many of the same benefits as freelance writing. This additional step is risky, though, because it requires marketing work to your target audience so they'll buy your work.
As with any sort of real career, networking is key. Freelancers are keenly aware that at any given moment, one gig might dry up, and if money's tight, that's a problem. Developing a group of consistent clients is a way to ensure that you're actually making (and saving) money as you work.
Writing's not the only way to make money freelancing, of course — anyone with graphic design or programming experience can find contract jobs that pay well and provide challenging work, too.