When you activate an ability, you untap the creature with that ability as a cost. The untap can't be responded to. (The actual ability can be responded to, of course.)

If a creature with an ability hasn't been under your control since your most recent turn began, you can't activate that ability, unless the creature has haste.

If the permanent is already untapped, you can't activate its ability. That's because you can't pay the "Untap this permanent" cost.