A common mistake I see artists making on facebook and other social networks is joining an artist networking group and then just posting their artwork, where it mostly gets ignored..
Why? Because everyone else in the group is an artist looking to promote their OWN work!

The fact is the majority of your potential audience will more than likely NOT be artists or in artist groups... Your audience will be in other groups, where non-artists congregate.
For instance, I have determined that the main market for my commissioned portraiture is middle to high income women in their 30s to 50s.
I can reach this audience much more efficiently by targeting yoga groups, neighborhood groups, parenting groups, decorating groups and new age spirituality type groups then by posting my work in photography or “share your art” groups.

And this is key - I don't just join and immediately spam them with my artwork. I start out by joining in conversations and in the course of contributing and conversing, I mention that I am an artist and then I can link to my facebook fan-page or post a picture of some children's or family portraits I have done... All of this is in the course of an online conversation. The trick is - you have to participate in discussions . No one likes a spammer - online or off!

Social media rewards “sharing” and penalizes self-promotion..