If you PC does not have the icon My Computer you may instead have the icon Computer  (again either on the Desktop or on the Start Menu), this will generally mean you are running Vista. Right click on the Computer icon and left click on properties. The following window should appear:

As you can see, Vista's system properties window is very different from that of XP. Vista not only gives the version of the operating system ,in this case Home Premium, but also gives a rating which is based on the hardware of the computer.

There are other ways of finding out what version of Windows a computer is running on but the above tends to give more information than most.