Downloading to the ereader depends a little on the eReader.
Some very basic eReaders, and Kindles, do not support Adobe DRM, in which case you cannot read such books on that reader.
Most dedicated eReaders should show up in the left panel of ADE when they are plugged in to the USB.
You might need a special driver, eg for Sony eReaders a driver is installed with the Sony Reader software.
Some don't work correctly on ADE2.0, in which case try using the older but more reliable ADE 1.7.2 instead (see bottom of post).
Once the eReader does show up in ADE, you will need to authorize the eReader (menu-Library-Authorize Device on 1.7.2, setting to the left of the device in 2.0).
You should then be able to drag-drop books onto the device from within ADE.
For tablets uses as eReaders you need an appropriate eReader app.
Post again if your ereader is a tablet.
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Version 1.7.2, it is a little difficult to find, available on Adobe site for Windows and for Mac.
http://helpx.adobe.com/digital-editions/kb/cant-install-digital-editio ns.html
The forum software is sometimes corrupting the link above. There shouldn't be a blank in 'editio ns.html'. The following redirects to the same page: http://tinyurl.com/diged172