What should a Muslim say when he offers an udh-hiyah (sacrificial animal for 'Eed) and dedicates its reward to his father, for example?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

When one offers an Udh-hiyah on behalf of his father, he should say (at the time of slaughtering): "Bismillah Allaahu akbar. (In the name of Allaah, and Allaah is the Greatest). O Allaah, that is on behalf of my father." He should hold the intention with his heart as well. It was narrated that when the Prophet, sallallaahu ‘alayhi wa sallam, finished his khutbah (sermon), he stepped down the pulpit, brought a sheep, and slaughtered it with his hand, saying, "Bismillah Allaahu Akbar. (In the Name of Allaah, Allaah is Greatest). I am slaughtering this on my behalf and on behalf of whoever cannot offer an udh-hiyah of my ummah." [Abu Daawood and At-Tirmithi]

If you mean that the person offers an Udh-hiyah on his own behalf and dedicates its reward to his father, then, after slaughtering, he should say: "O Allaah, if You have accepted my sacrifice, then give its reward to my father." Or something to that effect.

Allaah Knows best.