This article is by Clint Watson, former art gallery owner/director/salesperson and founder of FineArtViews. You should follow Clint on Twitter here.
Every artist needs to pay attention to the concept of the "circles of marketing."
Ignoring it leads many artists to make one of the biggest mistakes that I see in art marketing: thinking that art marketing is a "numbers game" and focusing on "getting traffic" and "eyeballs" before mastering the more important and more accessible parts of marketing art.
This mistake leads to artists worrying about things like "SEO" before they even learn to take care of their existing fans and closest supporters.
Here is the concept: Seth Godin posted the following image on his blog, along with his post, The Circles of Marketing:

The mistake artists make is the same mistake many people make. As Seth points out in his first sentence, "Most amateurs and citizens believe that marketing is the outer circle."
But "marketing" is not only or even mostly the outer circle.
I can't give you any better advice on how to market and sell your art than Seth's last sentence, "When in doubt, when your (art)* marketing isn't working, the answer is easy: go one circle in."
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* The word art added by me :-)
via faso.com
I was just reading another topic and two of the artists who had commented started their careers as scientists. There's a story for you. Every artist has a story of how they ended up in the art world.
Every piece of artwork has a story too. Communicating these stories is what's going to make people connect with an artist and their work. Today, thanks to blogs, everyone can tell their story.