I had a few people over time who have come to me because all of their icons disappeared of the desktop. The solution is simple, right clcik on the desktop and click on view.
Then check the last option down Show desktop icons. If you have a cluttered desktop and want to hide your icons then just check it.
You also have a few other options here. You can change the size of the icons.
Auto arrange icons: will line up all icons on the left hand side of the screen. Uncheck this if you are trying to move icons to somewhere else on ypur screen but they keep snapping back to the left hand side.
Align icons to grid: You can move them anywhere but this helps you line them up more neatly.