I haven't made any sale, but I'm just starting out again... I'm studying up on Internet Marketing... and here's what I learn, which could help with selling your artwork.
Find a spot to sell your art - Zazzle, Etsy, DeviantArt, etc
Have a Website (optional) - There are places where you can get free hosting (but no domain name) such as Blogger.com which is run by Google. Or purchase your own domain and hosting, then download Wordpress. You don't have to be a web designer to put together a website with Wordpress (wish I knew this when I was younger).
Once you have your art up at either those place. All you need now is traffic.
Some of the places people mentioned are great, but I like Pinterest the best. Why? A lot of people go to Pinterest to get inspiration and often time buy things! A lof of the artwork I check out on Pinterest have been sold out! (Average price of sold items I've seen are 250+).
But before you can get your work sold through Pinterest, you must have a lot of followers. Active followers that are interested in art! That way when you Pin your work on your account, others will see it and if they like it, they'll Pin and their followers do the same. So if you don't have a lot of followers at the moment, I recommend start following people that are pinning artwork. I heard you're only allow to follow 200/300 new people a day. So do this for a month and you're following 6000/9000 people. The statistic I read is for every 100 people you follow, at least one will follow you back. Not sure how true it is...
Pinterest is a WONDERFUL way to get free traffic to your work!
I don't find Facebook useful for traffic, unless you're willing to pay facebook to promote your page. Otherwise, you're only getting friends and families to see your work.
Instagram is a nice place for exposure, but you can't link to your sale page through your post. Only in your profile pace (and not everyone will bother checking your profile)