Here are examples of your three usages of the verb "to face." To face: He needs to face his fears and just ask her out on a date. She should just face her boyfriend and tell her that she is sorry. You should face the front of the class when your teacher is teaching. Face up: You need to face up to the fact that you might never walk again after that accident. (British English? I would never use "face up" like this; I would just say, "You need to face the fact...") You should face up to your responsibilities. (Same thing here. I think you might use face up more in British English, but I would never use face up like this. "You should face your responsibilities.") He was lying down face up on the table. (Non-verbal) Lift your face up, so I can see your eyes. (Non-verbal) Face off: They waited anxiously for the faceoff of the ice hockey match to begin. (Beginning of an ice hockey match starts with a faceoff; non-verbal) The politicians were facing off in a battle that would last years. Two of the best teams in football are facing off against each other this weekend. In conclusion: Again, it is probably more so in British English, but you can say "face up to your fears/responsibilities/etc" whereas you would just say "face your fears/responsibilities/etc" in the US. Thus, "face up" generally means "to deal with something that you might be nervous/afraid to deal with." "Face off" deals with two opposing forces battling against each other. Politicians can face off in a battle of wits and manipulation. Armies can face off on the battlefield. Sports teams can face off against each other. Hope this helps! Best of luck!

If you give us some examples (such as the sentences where you saw these phrases), then we can explain it more easily to you.

I agree with Jake here. Americans do not normally use the verbal phrase "face up." If we do use it, it would be to confront something that is non-physical, such as one's fears or problems. It might be used as a verbal phrase more often in other English dialects. "Face Off" would be used to describe one or more animate or inanimate physical objects in a confrontation/competition/fight/battle with 1 or more animate or inanimate physical objects. So "face up" would apply to a interior or psychological confrontation, whereas "face off" would apply to an external/physical confrontation.