First, you need to search the badges to find one you're interested in. A good way to search is to click on tags and then view all. Once you find a badge you're interested in, click join badge. You can join lots at once! It will tell you the evidence that you need to submit to get your badge. Once you're ready to complete the badge, you click the "plus' to add evidence. You can do this over time as you finish the badge. When you're totally done with all your evidence, you click "request feedback" to try and earn it. Someone will look over your evidence and approve it.
