Arthur begins as a war-leader, not a king: the Historia Brittonum (ninth century) credits him with twelve victories including Mount Badon and calls him dux bellorum, and the Annales Cambriae record his last battle at Camlann in 537 where he and Medraut fell. Geoffrey of Monmouth's Historia Regum Britanniae (c. 1136) turns him into a king who conquers Europe and is carried to Avalon, and the Welsh Culhwch and Olwen already puts him at the head of a named warband. Chretien de Troyes adds the court and the Grail, and Malory's Le Morte d'Arthur (1485) fixes the Round Table, Excalibur, and the once and future king.
Modern Practice
There is no historical cult and no ancient rite: the modern practice is literary and devotional, and it is best kept honest as such. What is done is a candle at a standing stone or a hillfort, a shared meal at a table, a vow written down and actually kept, and the reading of a source text aloud rather than a film.