[Cdesja5]

You need to have ADE installed on the PC. When you click the Adobe DRM download button, a link opens for an acsm file, select save and when you click on it, ADE should open and load your book.
To get it into Calibre go to My Documents--> My Digital Editions folder, the epub (or pdf) is there.
If that's not working, I would uninstall and then re-install ADE. They are not stored anywhere else.
What error are you getting and at what point in the process?

I am assuming that you are trying to download from the Kobo website and clicking the Adobe DRM download button there from your description. If you are have installed and are using the desktop app, then what taming says applies...