Once you choose Edit, there should be icons that appear at the top of the document list for each of these functions. They will be greyed out if the function doesn't make sense for the current selection.
The icons are
Folder with + Sign : Create a Folder, only active if there are no documents selected
Two Documents : Duplicate Selected Documents, only active if there are 1 or more documents selected
Folder with -> : Move to folder, only available if there are 1 or more documents selected
Box with Text Cursor and ... : Rename, only available if there is 1 document selected
Trashcan : Delete, only available if there are 1 or more documents selected
If you don't see the correct buttons, there are two things you can do:
(1) RELOAD THE APP: Click the Home button. Double-click the Home button to view recent apps. Press and hold on the Adobe Reader app to view a delete (red minus sign). Click on the app, and it quits. Click the Home button and relaunch Reader.
(2) RESET YOUR IPAD/IPHONE: Click the Home and Wake/Sleep buttons at the same time. Keep them down past the Slide to Power Off message until you see the Apple logo. Let it come up and relaunch Reader.
If you want to delete a single document, don't bother using the edit menu. Just put your finger on the document in the "Documents" section and swipe to the right. This should bring up a delete button for that document.