First, you'll need to know what's what. The big open area on your monitor where you see icons and where programs appear is called the desktop. The bar at the bottom of the screen that includes the Start button, as well as buttons that correspond to each program, is called the taskbar. The boxed-off area on the right side of the taskbar where the clock and possibly some small icons are located is the system tray. The icons on your desktop, in the Explorer and in the system tray mean different things.
Most shortcuts have a small arrow in the lower left corner of the icon.
You can usually find out more about what they do by holding your mouse cursor over them, or by clicking on them with the left or right mouse buttons. The icons you see when you open My Computer are the files and folders stored on your hard drive. Your hard drive, by the way, is not the same thing as your computer's memory. The hard drive is where your programs and the documents they create are permanently stored. The computer's memory is where programs are loaded when they are launched.