Create an atmosphere of trust. At the beginning of each class, remind students that their work is their own and that they should feel free to express themselves in whatever way they see fit. While art class is for learning, it is also a place for self expression. If students don't feel free to create without judgement, it will seriously hamper their self-confidence and belief in their own ability to create art and meaning.
Focus on the creative process. Encourage students not to get bogged down worrying about the quality of their work or comparing their work to other students, but to enjoy the creative process and use art as a means of self-expression. By focusing on enjoying creation, students will feel free to express themselves without fearing judgement. In addition, this helps them keep their mind focused on learning and experiencing art without distraction -- which will build confidence as skill increases.
Teach simply. By teaching the basics of art in a way that is easy to understand, your students will be able to more quickly grasp the nuts and bolts of the artistic process. This, in turn, will give them more confidence, as they feel they understand and are able to effectively execute the concepts they are learning in class. Give them ample assignments, in and out of class, that will give them many opportunities to practice creating art and explore their own abilities.
Discourage negativism and comparison. Many students will express their lack of confidence through self-deprecation, verbalizing their fears -- "Oh, this isn't any good," or, "Wow, yours is so much better than mine." By refusing to allow this type of speech in your class, you will encourage students to be confident in their own work without comparing it to others.