He was married to Hildeburh, a sister of the Danish lord Hnæf, and was killed in a fight with Hnæf's lieutenant Hengest after Hnæf was himself killed by Frisians.
Here we reproduce a passage from Beowulf as translated by Seamus Heaney (lines 1089–1090):
As before about Sigemund and Heremod, so now, though at greater length, about Finn and his feud, a lay is chanted or recited; and the epic poet, counting on his readers familiarity with the story,a fragment of it still exists,simply gives the headings.
Finn, a Frisian chieftain, who nevertheless has a castle outside the Frisian border, marries Hildeburh, a Danish princess; and her brother, Hnæf, with many other Danes, pays Finn a visit.
That is, Finn would govern in all honor the few Danish warriors who were left, provided, of course, that none of them tried to renew the quarrel or avenge Hnæf their fallen lord.