Post your portfolio online. Make your own website, if you are skilled enough, or use templates that allow you to create a basic website featuring images of your art. Include your contact information so people can get in touch with you if they like your art. You can also add a shopping cart function to your portfolio so people can order your art directly from your website.
Research target galleries that may be interested in your art. Look for online galleries that sell the medium you work in, represent artists of similar styles, are reputable and promote themselves through various strategies. Make sure these galleries represent artists at the same level of expertise as you.
Send an introductory letter to your selected galleries. Request a critique of your work by sending them a link to your portfolio. If the critique is negative, you will know what to improve or that your style is not what they are looking for. If you receive a positive critique, ask them what it takes to advertise your artwork on their website.
Ask your friends and family to help promote your work. Show them your portfolio along with a sample introductory letter they can then send to people they know. Word of mouth will help bring you additional potential clients, and you may even make connections with people who are already heavily involved in the art community.
Use social media tools to build a community of fans and promote your work online. You can build a Facebook fan page, create a Flickr photo album of your art, create a LinkedIn profile, start a blog or tweet about your art. Or open a virtual shop on an artist-oriented site such as Etsy. Although these techniques are free, they can take a big part of your time. So use the social media tools you are most comfortable with, and limit yourself to the ones that allow you to get in touch with potential customers.
Connect with your specific art community online via forums and networking groups. Not only will this help promote your work and increase your visibility, but it also will help you create a circle of friends who share your passion for art and understand what it takes to make a living creating it. Online networking also helps you position yourself as a peer inside the creative community.