Generally, storing every random file that you recently played with on your desktop is a bad idea.  It quickly becomes a cluttered, confusing mess underneath your open applications.  Old habits die hard though, so here’s how to get your desktop icons back on elementary:

1. Hit Alt+F2 to open the “Run Application” window.
2. Type gconf-editor and hit Enter to open the “Configuration Editor” app.
3. In the folders on the left, navigate to /Apps/nautilus/preferences/.
4. Find the key titled “show_desktop” and check its check box.
5. Look! Icons under your open windows!

Note: This guide is for the current stable version, elementary OS Jupiter.