To download your badge, right click the image and select "Save image as...". Navigate to your downloads folder and open the image on your computer. From there you can print it or save it where you would like.
Here are a few ideas for displaying your badge:
Print it out, use it as a template to cut a piece of carboard matching the shape, and then glue the paper and a pin onto the cardboard.
Use tape to secure it into your park passport or scrapbook.