How was the story Beowulf originally told?

It was Written because it was a true story and they wanted other people to know about it (what happened) in our days and so on.

I'm going to leave this answer up, however, it is quite a terrible attempt at an answer.

1. There's no way, currently, to verify the accuracy of the events in Beowulf. However, many of the battle scenes are not likely to have occurred as written, especially any underwater battles.

2. The real question of why Beowulf was written is far more complex than "they wanted other people to know about it." You'd have to define they. They is/are whoever wrote the story in Old English. Which is an odd thing once you consider that the Anglo-Saxons were not good friends of the Danes. This meant 1 of 2 things. Either...

a. A Dane who knew Old English decided to write a piece about a Danish hero as Propaganda, or someone who really didn't know their target audience.

or...

b. An Anglo-Saxon wrote a story about a Danish hero.

Both theories beg the question of "Why?"

There isn't a definitive answer. Especially not: "because it actually happened," and someone thought to themselves, "SURELY people hundreds of years from now will find this important." Also taking into consideration that paper and ink was made by hand. This would mean that to produce one copy of Beowulf would be to kill an animal; prepare its hide for use; make their own ink; and write and reproduce Beowulf by hand. Each copy. So, I really don't think the answer is as simple as the question.