No elf prays to the Undying Court, it is merely a name for the religion of ancestor worship in Aerenal.
The Aereni people honor and revere their ancestors and forebears, including living elders. Elves who follow the Undying Court often pray to and swear oaths by their ancestors, usually calling upon a particular individual who has influence that applies to the situation at hand.
The Undying themselves are granted their immortality as the greatest honor that can be bestowed by the Priests of Transition. The other, more common, honor granted is for an elven spirit to be bound to his or her embalmed corpse or reliquary so that he or she may commune with the living in times of need.