You can pay either the morph cost or the creature's normal mana cost to flip it up.
Manifest is covered in Mechanics of Fate Reforged. The relevant snippet for this question:
If you happen to manifest a card with morph, you can turn it face up either by paying its mana cost (if it's a creature card) or by paying its morph cost.
In general, when you have a question about a mechanic from a new set, a really good place to find answers about it is the mechanics article Wizards posts for the set. The title is always in the same form as this article ("Mechanics of {set name}") so they're really easy to search for.
If you want the full technical details, the comprehensive rules are the place to go (see Rainbolt's answer), but if you want a practical, easy to understand answer, these articles are really useful. As a bonus, they're often published a bit before the comprehensive rules updates, so you can satisfy your curiosity sooner.