Long-press an icon (hold it down with your finger) until the phone vibrates. Now, without lifting your finger, drag the icon down towards the tray button. It will turn into a garbage can. Drag the icon on to the garbage can and the shortcut will be deleted from the desktop.
To rearrange, do as above (longpress) and drag to where you want it, then let go. To get it to another screen, drag it to the edge of the screen and it will flip to the next screen.