How to add a contact to People from Hangouts? I'm using KitKat. I have Hangouts conversations with people who are not in my contacts (this may be an artifact of using a Google Apps account provided by my school). How can I add someone from one of these conversations to People?

I have tried double-tapping and holding down their icon or their chats without any success, and looking at the "..." options menus. No luck. I do know how to add contacts from email.
View the Hangout of the unknown contact
In the lower left hand corner of the Hangout screen, you'll notice a small icon to the left of the text box. If you tap that, 2-3 options will be available: "Hangouts," "Mobile (via SMS)," or "Mobile (via Google Voice)."  Select "Mobile (via SMS)."
Open the overflow menu (three dots in the top right corner) and select People &amp; options
At the bottom of the people &amp; options menu, you'll see "People in the hangout." The phone number should say 'touch to add to contacts'. Touch it. 
Either search for an existing contact and add the new number for that contact or you can add as new contact by using the three dot overflow menu.