It sounds as if for some reason Adobe Digital Editions has not been able to make the correct file associations.
There is a bug in Windows 7 and 8 that causes this problem for quite a few people (but not all WIn 7/8 users).
Even resetting it explicitly from the Explorer 'open with' dialog does not work in that case.
Try using a third party app such as http://www.nirsoft.net/utils/file_types_manager.html to make the association of .acsm and .epub files to ADE.
As a one-off, you can open ADE and then drag-drop files from a file manager such as Windows explorer onto ADE.
For .epub file you can use the standard menu-open (ctrl-O), but this doesn't work for .acsm files.