In Beowulf, the protagonist of the same name travels to the land of the Danes to aide them in fighting a monster who has killed many. Because of his extraordinary strength and courage, he is able to defeat Grendel in bare-handed combat. After he receives the rewards for his victory, he also has to fight and kill Grendel's mother as she is also causing havoc. After successfully slaying them both, he returns to his homeland with an overwhelming amount of riches. Later on, he becomes the king of the geats and has to fight a dragon that's threatening the kingdom. He ultimately kills the dragon, but received mortal wounds in the process and dies.
Therefore, the order of the events is as follows:
Beowulf sets out on his journey for Daneland.
Hrothgar welcomes Beowulf.
Beowulf waits for Grendel to attack Heorot.
Beowulf succeeds in defeating Grendel by tearing off his arm.
Beowulf fights with Grendel’s mother.
Beowulf sets out for his Geatish homeland.
Beowulf sets out for his fight with the dragon.