Search through online art communities like Deviantart.com, asingularcreation.com and dominancewar.com. These communities sometimes host contests themselves, and they sometimes have forums or blogs where individuals advertise contests.
Scan the the guidelines and look for the phrase "registration fee." If there is no registration fee requirement listed, this contest likely does not have a fee.
Decide if the prize is worth the time taken to create the artwork. Art takes a lot of practice and hard work, and an artist can always benefit from the motivation that art contests provide, even if you do not the contest. Some contests do not offer a prize at all, but these contests can provide artists with helpful feedback, as visitors can often comment on the artwork.
Create the artwork following the guidelines for the art submission. Some art submissions must be done through a particular medium, like acrylic or water paint, while other contests only accept drawings and artwork that focus on a particular topic.
Determine how the art is supposed to be submitted. Some contests ask for a hard copy of the artwork, but most free contests ask for a digital file. The file should be in a .jpeg, since this file can be read by most programs. If the artwork is created through traditional means, the art can be scanned or photographed with a digital camera.