Do you belong to a co-op gallery?
Quite often co-op galleries are quite happy to link from their website to their members' individual art websites. Since the business model is that of a group working together to make the co-op successful and members have a vested interest, they are often much more willing to do this than a traditional gallery would be.
If you belong to a co-op gallery that's willing to link from their website to yours, take advantage of this oppurtunity.
If you have profiles for your art business on social media sites such as Facebook, Twitter, LinkedIn, etc., make sure you include a link to your website.
Social media sites get lots of traffic from search engines because they are huge sites used by millions of people. This doesn't necessarily mean you'll get lots of traffic, but every relevant link helps. Just make sure you set your profile to "public" because the search engines don't index pages that are marked private.
See this post about creating a separate business page on Facebook so you can keep your private and professional worlds a bit more separate.
Are you a member of a professional artist guild, arts alliance, or other art related group?
Does this group have a website?
Many of these types of groups have a website with pages for artists' personal profiles. You should participate in this profile page if offered. And, make sure your profile page includes a link to your personal artist website.
Many of us do retail art shows - but many don't take advantage of the (usually) free link to our websites that the shows offer.
Make sure when you fill out your show application, contract, publicity materials, etc for the show that you fill in any field that asks for your artist website address.
Free advertising! From a large, well publicized website! - Why the heck would you turn that down?
Links going out from your website to other related websites are a much overlooked tool for improving your results on search engines like Google.
By linking to other sites, you are networking and building your own relevence. Pointing to outside sources makes you look good - you are participating in this thing we call the world wide web. Just think of how social media works - millions of people sharing links.
By becoming a source for information, you increase the chances of other sites linking to you, which in turn can help increase traffic to your site.
Read more tips for attracting more traffic to your website
Tip #1 – What You Write is Important
Tip #2 – Be Specific
Tip #3 – Be Local
Tip #4 – Talk About Your Art
Tip #5 – Get Other Sites to link to Yours
Tip #6 – Some Links Carry More Weight
Google’s Matt Cutts discusses the issue and how good content leads to good links.