Here are a couple of videos that might help (replace the library websites in the video with your libraries site)...
http://www.youtube.com/watch?v=_9OxDGpEGeY
http://www.youtube.com/watch?v=bz0OcjgxtSU
These are for borrowing Kindle books, if you're trying to borrow ePubs to read with the OverDrive app or another app like Mantano, Aldiko or BlueFire the steps are a bit different.