Beowulf is a classic tale which has been translated many times and has had many film adaptations. Seamus Heaney's new translation and Frederick Rebsame's translation are good starts if you have not read it yet. Of course, it was one of the inspirations of Tolkien's Legendarium. It's a timeless story that has been replicated to some degree by many other media over time.

What is a step-by-step process to adapt a story, for example Beowulf, into a game scenario?

It does not necessary need to be the exact same story, you can (read: should feel free) to get the main themes from Beowulf into a story. I am looking for methods of how to adapt literary works to role playing adventures using Beowulf as an example. The RPG in question might be far afield from what you'd expect (like using Beowulf as source material for a Shadowrun, Toon, or Eclipse Phase game instead of medieval fantasy).