Identify a problem space, evaluate products that try and solve/work in that particular problem space (against some best practices/design principles), and then ideate some solutions/products of your own.
Document HOW you approached the problem space – many times the approach and rigor that you show in your process is as or more important than the final solution if you are trying to get a job/break in to UX.
Finally, be open and honest about your abilities – showcase your best work, and accept criticism gracefully. Show a willingness to learn. Basically be humble, and confident at the same time. How? I don't know… fly casually!