This is what I get in the Get Info dialog box after doing what either you Barnie-15E suggested, or what the Apple Help information suggested, which is essentially the same thing.
What I was trying to do was to create an alias to open the Apple Support System web site page, which shows you the status of the various Apple services that shuttle emails, messages, files etc between Ios and Mac devices. I wanted the Icon of an Apple logo instead of the Safari logo that was automatically created when I made the alias by bookmarking that web page. In other words, I wanted the dialog box to look like THIS, indicating that the logo was going to be the colored Apple logo on the associated desktop icon:
The only way I could get such an icon was to go to an "icon maker" program I found on the web, have it create a .icns file of the colorful Apple logo from a logo picture and bring that back to my computer, then Drag and Drop that file onto the existing icon image in the Get Info dialog box. If I tried to Copy and Paste that icon file using the procedure in the Apple Help it produced an image that said ICNS. If I tried to Copy and Paste the Apple icon PICTURE, then I got the JPEG image as shown above. The only thing that worked was to Drag and Drop the .icns file, which produced what I wanted as shown above, which makes THIS desktop alias (below) that suggests visually *to me* that it opens the Apple suport system's Status page. They seem to have changed something since the Help article was written; it is also wrong in the Pogue Missing Manual book on OS-X for Mountain Lion.