Left click on the link on the desktop. You will get a drop-down menu. Click on Properties. You will get a dialogue box. At the top, there will be a blank box (button?) and a text box with the name of the link.
Left click on the box (button) on the left, and you will get into the system default icon directory. You should have the option to browse for other icons in other locations.
To find other icons, open a term window and issue the command: 'locate icon | less', without quotes. That will get you a listing of all directories with the expression 'icon' in the name. Write the name of the directory from which you want to choose an icon (with full path) into the browse text box from the Properties dialogue, then choose the icon from your chosen location. Finish the process with whatever buttons are provided to you, and you will have a new icon on the desktop.