Icons disappear from desktop or show up twice

I was trying to move imported doc files from the main user account to public
folders so the other users with accounts on my computer (the rest of the
family) could see them. In the process I seem to have caused a problem with
my desktop. All my user icons appear twice or sometimes not at all. If I
try to delete the extras, both in the pair disappear. If I restore from the
recycle bin, one comes back, for a time, but the next time I log in it's back
to twice or none again. An IT guy at my office mentioned something about a
virtual desktop.

Any ideas what I did and how I can fix it?