Basically anytime except for when you speak to your close friends, family, and children.
Especially, when you speak to someone
- who just met or don't know each other yet.
- who is in "higher" position than you, such as teacher, president, boss, customer, etc.
- who is older than you.
Actually, honorifics could be added here, there, and anywhere...
Here are some basic ideas:
-Use -masu/desu style speech. For most cases, this would work enough for you to be polite.
-Put honorifics to nouns and actions that belong to the person to be respected.
(example: anata no "o-namae")
-Use humble forms for nouns and actions that belong to yourself. (example: watashi no "namae")
Hope it helps.