ClientCare isn't providing support on Analysis Workspace yet, while it is in public beta.
It turns out I am only partially right. You can't drop an entire dimension onto a column header yet. That's planned for an upcoming release.
However, you can add specific dimension values as columns. To do this, mouse over the dimension that you want (in the left rail). You should see a right-pointing arrow appear to the right of the dimension name. Click on that. You will see the dimension values, and you can then drag them over as columns.