It’s pretty easy to delete a Broadcast (remember they last 24 hours in Periscope’s server before they are deleted automagically).
Step 1: Once you have finished (Uploaded) your broadcast you will see it in the Recents Broadcasts section (or in your Profile as well), just Swipe left and Tap the Delete button.
As simple as that. Let me know if you have issues or something so I can come up with something to help the community.
PS: Most of the tips I give here are for iPhone (iOS) unless I comment otherwise or I put both versions methods in the post. Happy Periscoping!