You don't install ADE on the ereader, it already has the necessary software builtin (assuming it is one that supports Adobe DRM),
- plug in the ereader and run ADE (Digital Editions)
- If all goes well, when the ereader is plugged in it should show in the left panel of the Library section in ADE.
- Authorize ADE with your Adobe ID (menu/Help/Authorize Computer on v2.0, Library/Authorize Computer on the older more reliable 1.7.2)
- Authorize the ereader (menu/Help/Authorize Device on v2.0, Library/Authorize Device on 1.7.2)
- Drag books from your ADE library onto the device in ADE; that should copy them across
- You should now be able to read them on the ereader when the ereader is unplugged
If any of those steps fails, post back to say exactly where it failed, and what message you got.