The UI has changed since my answer on May 21. The Batch button is gone and there are now two views - Grid and List. To switch between these use the buttons just to the left of the Sidebar.
From Grid view you can click on the triangle to the right of the file name below the thumbnail. This will give you two options: Move (to a folder) or Trash.
From List view you can check the box to the left of the items you want to take an action on, and there is a Select All check box at the top. As soon as you check some items you will see the same two options appear: Move (to a folder) or Trash.
Once you have Trashed items you can switch to the Trash View using the trash can button that is next to the grid and list view buttons. You can then Permanently Delete files or Restore them.
