Is this a dedicated ereader, or a tablet with ereader capabilities.
A dedicated ereader should show up as a device in the left pane of ADE (Digital Editions).
You must then register the device, Make sure ADE itself is authorized, then use 'menu/Help/Authorize Device' ('Library/Authorize Device' on the older more reliable ADE1.7.2)
Most tablets don't get seen by ADE at all.
You need to install an Adobe DRM compatible app (Bluefire seems most reliable, there are also Aldiko and Overdrive) and register that with your Adobe ID.
Then transfer books from then computer using file manager (Windows Explorer, Mac Finder) to the tablet which should show up as a mounted drive when plugged in by USB.