So here's the dirty little secret about websites: websites are PASSIVE. They don't go out on their own and do your marketing for you. As a result, you can't just put up a website and expect traffic or sales to magically roll in.
You are your own brand and you need to promote yourself. Apple, McDonalds, Coca Cola, Nike, etc. don't just rest on their laurels and expect sales to roll in - they market their brands relentlessly. What makes you think you can avoid marketing your artwork and still have sales?
I always compare a website to a business card. You can have a gorgeous card printed but if you never give your cards out to anyone, they don't do anything for you.
Both websites and business cards are tools and tools are meant to be used - ACTIVELY.
Ok, so we at Art Studios Online (or some other website company) built you a nice, well-formatted site. And, we even let the search engines know that it's there. You're all set, right? Wrong!
You have to actively participate in this venture as well.
First, you supply content. After all, your site is about YOUR artwork. You need to supply both pictures and text that demonstrate what it is you do. And, unfortunately, search engines can't "see" your pictures - so this means you need to have text on your website that talks about them.
Next, you need to promote your site online.
Get links to your site from other art related websites. Do you belong to an art group or guild? Are you a member of a co-op gallery? Do you participate in art fairs? These are all good sources for links to your website.
Do you participate in social media? Promote your site on Facebook, Twitter, LinkedIn, etc. Talk about your art and events related to your art career on these social platforms and make sure you include a link to your website.
Finally, you need to promote your site in the offline world as well.
Have your website address printed on all your business related materials. Make sure you never leave home without your business cards and for heaven's sake give them out.
Take the opportunity to talk about your work in social/business situations when appropriate. I'm not talking about being that annoying woman on the plane who pulls out 900 pictures of her grandkids. But quite frequently, people will ask what you do - so take advantage of this and have your "elevator speech" ready. Often it will turn into a more lengthy discussion because many people are fascinated by the idea of the artist's life.
And, if they're really interested, give them a card, offer to show them around your studio, invite them to your next event. You know - network - it's how it's done in every other industry.
A website is just another tool in your marketing/networking toolbox not a replacement for it.