Be sure to have them do the following:
First, check to see if the device is compatible with overdrive e-books by having them go to the following links
Compatible devices: http://www.overdrive.com/resources/drc/Default.aspx?type=ebook
Incompatible devices: http://www.overdrive.com/resources/drc/Incompatibledevices.aspx
If their device is not listed on the compatible page or is listed as incompatible, they will not be able get e-books on their reader
Secondly, if their device is listed as compatible, have them verify that the date and time on both their computer and device are one in the same. If they are not, have them change it so that it is.