How do I edit contacts in Android 4.4?
Don't use the phone/dialer app to edit contacts: use the main People app (it's called Contacts on some non-Nexus phones). From that app, when you click the contact you want, it displays that contact, and you can click the pencil icon on the action bar (at the top) to edit the contact. (The icon might look different on your phone, because most manufacturers replace the People app with their own variant.)