ShawN shawN • Good question Janice. My advice is to build up your network. You already are on Linkedin, so that is a great start. You can connect with all your known art contacts, business contacts and other galleries. It is important to list your website and your portfolio on LinkedIn to generate more interest here. You can also build up the event in Linkedin and use that as a separate marketing tool.
Another great site to use is Evite.com. You can import your contacts from several email programs and then create a professional looking evite to send via email to your contacts. I always do this for every event.
As mentioned above, using Facebook and Google+ are excellent venues to advertise. FB is still much better than Google at this stage. Other venues are tumblr, stumble on, MySpace (still used a bit), twitter, etc.
Twitter is a special case because you can link twitter to your website, FB, Google+ and MySpace, so your micro blog is carried to multiple people. Always use keywords with a hash symbol like #art #painting #gallery #artshow, which will help unknown people looking at that to find your event. Use the @ symbol to send to particular people @obama for example. Another cool feature is to piggyback on popular trends of the day into your event if you can find a tie-in.
At the event itself, I would bring a camera and take as many shots as possible and film the event as well. This creates a good vibe at your event (you may be making them famous). Additionally, if you can have someone interview you on an android or iPhone, you can make it into a movie and upload to youtube for a multiplier effect of marketing of the show. Anyone that missed the show will get to enjoy it online and get psyched to see your next show. You can see my video as an example here: