There are numerous ways in the web 2.0 world to make money online with your art. many of the methods I will outline will also double for crafts and photography, but this primer is focused on traditional paper/canvas art and illustration. Both fine art (the fancy stuff) and simple illustration can make you money online two ways-selling it outright, or licensing it. There are many great websites that can help you accomplish either:
Your own website: Although you could certainly make money with your art without, I highly recommend having your own website to showcase it whether or not you are just an amateur dabbling in selling&licensing art such as myself, or certainly if you are a professional
who is looking to support themselves entirely with income from their artworks. Basically, your website will act as your home base linking all your social networks you will use to sell your art, and as well to display works, some information about yourself, and maybe even an e-commerce platform from which to sell your art. There are many e-commerce platforms available, but that is some what beyond the scope of this article. Ask your web developer about how to have your website enabled to receive payments, or simply Google "Website shopping cart system".
Selling: There are literally hundreds of websites to sell your art through, but I will go over some of the better ones.
eBay

Ebay, the site that started out for people to sell collectibles and knickknacks, is still a good place to start for selling your art. Although they don't specialize in art, you may already be familiar with the site, and it has a huge market of people looking for art on it. You can list your works either as a fixed price "Buy Now", or put them up for auction.
etsy.com

Etsy is specializes in all "artsy" and handmade things, and this certainly includes your
fine art and illustration; whether it be on paper, canvas, or a porcelain bowl. Etsy can connect you with a staggeringly big art market, and is great to use for carving out a niche. Inc Magazine did a great piece on how to use Etsy awhile back that I recommend: Inc Etsy Piece and I also recommend the book on the right.
Licensing & Merchandising:
Licensing-or sometimes you'll hear "merchandising- is when you simply sell someone the right to reproduce images of your art, but you retain the original. Here is an example from my Zazzle store, I made a one panel cartoon awhile back about being from Boston, and I have licensed it to Zazzle.com to be printed on postcards people can buy, when people buy a postcard, I get a royalty from the sale.
CafePress.com
CafePress.com is probably the biggest merchandising and licensing site. You can use them to put your art images on hundreds of different products that you can then sell
for royalties. I use them myself for both my Dimwitz Comics, and also my fine art. Take a look at my store to see an example of what one looks like: cafepress.com/dimwitzcomics. You can use them to sell everything from coffee mugs to actual prints, and many things in between like clothing. A lot of people say that CafePress' image quality can be low sometimes, and I agree but I'm sure they are working to improve it. Being able to see your image on a finished product is great though.

Zazzle.com is basically the the same exact thing as cafepress, and which one is better is a hotly contested issue. A Google search for "Cafepress vs. Zazzle" reveals endless arguing back and forth over which is better. I have used both sites, there are things I like about each, and things I don't. It really comes down to personal preference. I will say the first time I ordered some postcards off of Zazzle, they didn't come as had been pictured. I do like the sites ease of use over Cafepress, and that they allow more freedom in customizing the products.

Below are some up and coming clones of Zazzle and CafePress I know little about for now:
ImageKind.com

Printfection.com

Art Marketing:
You can have the best website ever, and be on all of the above art platforms, but it will still behoove you to learn all you can about art marketing. It will be hard to be successful with your creations without some marketing savvy. For starters, I recommend reading my article on marketing tips for selling online: Bonobos Pants Case Study.
All artists and illustrators, no matter what they do, they should own the most current copy of the artist's and graphic designers market:

EmptyEasel.com
Empty Easel us a great all encompassing source for how to market art on the internet, plus they have an easy to use art submission form.

DeviantArt.com
This is an online community of artists where you create a profile and promote your works. It seems to be better suited for a certain style of art-more underground stuff if that makes any sense.

Taking Good Photos: If you are going to put your art on the internet in anyway, it's really crucial to learn how to take great images of you art. I recommend this article by empty easel: Empty Easel on photographing art.
Social Media/Networking Sites:
I recommend all the major social networking sites for selling your art, facebook, twitter, pinterest etc. These sites are great way not just to promote your actual works, but to find and engage with other artists and potential customers alike. Pinterest is especially good as it is an image based social media network where people "pin" images-especially art-that they like. You will want your website to include the pin tool so people can add your art this way. Read my article about it below.
For a more comprehensive look at Pinterest, I recommend the book
Pinterest for Business by Jess Loren and Ed Swinderski. Full disclosure, I am scheduled to be potentially quoted in the book myself. Click to pre-order it at Amazon.com