Drag & drop them onto the Library icon. That's my prefered way of doing it.

Oh hold on, you're trying to drag them from LW are you? I thought you were trying to drag them from the download folder after opening it up.

Also, I like to have the Date Added column showing in iTunes. You can find that under the edit or view menu I can't remember. Then click on the Library icon so it displays the entire library. Then click on the top of the Date Added column heading so it arranges the library songs with the newest added listed at the top. That way I can be sure they were added ok.