How much do you know about file permissions and what kind of tricks have you already tried?
If you're not sure who owns the file, right-click on it and look at the properties, or alternatively open a console and type
CODE
ls -l Desktop/
(list the contents of the Desktop directory in
long format) - and post the result here if you're still not sure. This should tell you who owns that file, and also who has which permissions to access it. You'll need "write" permissions in order to delete it or move it to Trash.