When you download from the library your browser should try to download an acsm file. The default option should be open with ADE (you can also use the Sony software and the books will be stored elsewhere). When you do that ADE will open and the book, pdf or epub, will be downloaded. It should go to the My Digital Editions folder in your Documents folder. You should be able to either use ADE to make the transfer, use the Sony software to make the transfer or just drag and drop the book file to the proper location on the reader.
Here's a tutorial using the Sony software...
http://ebooktest.blogspot.com/2009/0...ng-public.html