Heather M’s Answer
It really depends. If you have friends and family who know you paint, it can often be a good start to practice on them so you can figure out if you like it. You may have been creating art for fun or pleasure for a while now, but it gets to be a whole different ballgame when you're working on things commercially. You have to be very receptive to feedback and criticism. You may feel that what your client is asking for is the most ridiculous idea in the world, but it's your job to paint it!
As with any freelancing, it's often very competitive and it's challenging to get your name out there. Fortunately there are a lot of different websites and things now that allow people to post jobs and connect artists with work. I'd search Google for freelance sites and contract artist sites. I've never personally used any of these, however. I just know they exist. Similarly, you may find something in your local classifieds.
Another thing I see these days is artists posting work on Etsy and writing up that they'll do custom work, or artists posting auctions on ebay for custom paintings within certain requirements. Again, I haven't tried these things - I've just seen them.
The one benefit you often have with going through a site with its own terms and conditions is that there's often something to protect you from non-paying buyers and the like. Do you research when you join any site and be sure the terms are fair and you agree with any fees involved with selling your work.
When you're working on your own, an aspect that's extremely important and often overlooked is your business side. You need to research how to write up estimates, contracts, and invoices so you're getting paid for your work! For example, some folks set up agreements where half is paid up front and the remaining half is paid when the project is complete. A contract ensures that the client has entered a legally binding agreement to pay you for your services. The bottom line is, if you try to run your freelance operation on good faith alone, you will likely be burned. Definitely research all of your operation details ahead of time. Some folks even have a lawyer involved to be sure their contracts and documents are legally sound.
Lastly, if you're serious about freelancing, you'll want to create a website portfolio to showcase your existing work. Often clients want to get an idea of whether or not your style is on target with what they're trying to do. If you show a variety of work, you can prove that you're a flexible artist who can work in a variety of styles. If you have a website, you can also market yourself more easily.