You can switch out badges icons from a predetermined library of artwork we provide or use your own. Our library of icons is available via the Tools tab of Site Center. Let us know if you need a badge icon you don't see there.
Right click on the icon you wish to download and choose the option to "Save image as...". Note, the exact wording of that option will vary from browser to browser, but it should be obvious which option you need to click.
Once you have the image on your computer, you can drag and drop it onto a badge module.