To put Google on your desktop, open Google in the normal way on your browser, and when it loads, click on the padlock/E sign you see at the beginning of the Google address on the address bar and drag and drop it to your desktop.
You can also download one of the Google desktop icons available freely on the Internet and place it on your desktop where simply by clicking on it, you can reach the Google homepage. Otherwise, copy this line (address to the Google home page): http://www.google.com/, and with it copied, go to your desktop and right click. Select "new" and then "shortcut" and past in the copied link. After clicking "next," type the name "Google" and click "Finish."