It depends somewhat on the operating system you are using. (That information would sure help.)
On Windows XP, RIGHT click on the desktop, choose "Arrange Icons By", then UNCHECK "Align To Grid" and UNCHECK "Auto Arrange" by clicking on them.
On earlier version of Windows, you should be able to RIGHT click on the desktop, select "Arrange Icons", and UNCHECK the "Auto Arrange" selection.
Hope this helps.
I accidentally pressed auto arrange for my desktop icons and they seem to be locked in place. Someone please remind me how to unlock them so I can group them in various areas on my desktop. I just haven't done this in years.