Upload to your plugins folder, usually wp-content/plugins/
Create category image (with .png extension unless you specify the extension in your call to c2cthecategoryimage()) for each category you wish to have an image for, placing the image into the wp-images/ directory (unless you specify another location in your call to c2cthecategoryimage()). Remember to give the filename the nice-name version of the category name.
Activate the plugin on the plugin screen
Modify your index.php at a point within "the loop" to make use of the function (assuming, of course, you've already defined categories and assigned posts to them).