Once you're in your Badge Library, which you can find under My Account, you have the option of sharing each badge by itself or your whole library.
To share your whole library, select the "Share Library" button on the top right and choose to share your library either through Twitter or Facebook. You can also copy a link to your badge library that anyone can see if they use your link.
If you want to share just a single badge instead, select a badge and select the "Share Badge" button under the badge details where you will have the same options to share your single badge as you do with your library.