First check if there is an appropriate .acsm file in your downloads directory.
then open ADE, and drag drop that .acsm file from Windows Explorer/Mac Finder onto the running ADE.
If that works, then ADE is basically working but the file associations are wrong.
If so, follow details below.
If not, post back.
Sometimes the registration of ADE to Windows as the default hander for .acsm and .epub files does not work;
that is what causes the double-click in Explorer to fail; and usually prevents opening from the browser as well.
especially in Windows 8/8.1, and maybe 7;
this appears to be a bug in Windows (for once not a bug in ADE).
Two possible ways round it.
First, try to force it in Explorer
Right-click on a .epub file (and repeat entire sequence for .acsm if necessary)
Select 'open with' if on the list, 'open' if not.
Select 'choose default program'
Select ADE if it is on the list,
If not select 'more options' and select ADE is on that list.
If not, at the bottom of 'More Options' list is 'Look for another app on this PC', select that
and navigate to the ADE executable (may be at C:\Program Files\Adobe\Adobe Digital Editions\digitaleditions.exe)
Now .epub/.acsm files should be associated with ADE, and double-clicking should work.
Sometimes, Windows allows you to go through all that, but then refuses to make the association you have asked for.
In that case, the only way I know is to use a third party file association program.