Turning a face-down creature with megamorph face up and putting a +1/+1 counter on it is a special action. It doesn’t use the stack and can’t be responded to.

If a face-down creature with megamorph is turned face up some other way (for example, if you manifest a card with megamorph and then pay its mana cost to turn it face up), you won’t put a +1/+1 counter on it.

Megamorph is a variant of the morph ability. You can find more information on morph on cards with morph from the Khans of Tarkir set.