Below every post, you should see a 'share' link. Click on that and a popup will appear that has a link to the post (the link includes your user id in the URL slug, which is how SE tracks the number of visits using that link) and buttons that allow you to quickly post the link on Google+, Facebook or Twitter. If you want to post it somewhere else, such as on your blog or by emailing all your friends, copy the link and paste it wherever you want.
The badges were originally announced on the Stack Exchange blog, Announcer, Booster, and Publicist Badges, but the time limit requirement has since been removed