If its a program your going to need to go to (assuming windows xp) start>control panel>add remove programs. Uninstall it from there.
If your just saying its a shortcut on your desktop. Right click the shortcut and it will have the directory to the file like "c:/program files/file1". Just go to my computer, the c drive, program files, and delete file1. Then back on your desktop delete the shortcut.