First and most obviously, you should expect to write a lot. In most WAC courses, this may probably means writing both formally for assessment by your instructor and writing informally as part of your own learning process. Second, you should expect to have your work read and responded to by your instructor in a way that helps you improve either the paper you're working on or future papers, as well as to be challenged by your assignments. Third, those assignments should invite you to think hard about key concepts in the course and to practice using language and genres important to the discipline or to its practice in the field.
So in short, you should expect to write in ways that will help you both grow intellectually and understand what it means to write as a member of a discipline - an art historian, sociologist, or literary critic - and your professor's responses to your work should be an important part of this process.
Don't be surprised if your WAC courses also require you to do some other things - perhaps to participate in peer workshops, to spend some time in class analyzing models of good writing in the field, to meet with your professor to talk about your work outside of class, to do lots of careful, thoughtful revision, to contribute to some collaborative document like a course wiki, or to pay more attention to the fit and finish of your work than you may do in other courses. Your professor will be thinking about the best way to build writing into your course, and this may mean a range of activities and expectations. Be ready for this.