You need to make sure that your desktop is set for Folder View and it is set
for the Desktop location. If you see a clear plasma window on the desktop
with icons in it then you do not have Folder View enabled, but are in the
default desktop. To do that you right-click on the desktop (not the plasma
window) and choose Desktop Settings. Then on the Layout drop-down choose
Folder View. Folder View looks and works like the old KDE 3 desktop.

Once it is set for Folder View you can drag and drop icons from the Menu to
the desktop or If you right click on a menu icon then you choose Add to
Desktop. If it is not in Folderview and you have the default Desktop the
desktop icon will appear in the plasma window which still gives you the
launcher, but it is not as handy. If you are used to GNOME then Folder View
is better than the plasma overlay.