This is a very broad question. It can be daunting to be asked to write an essay on a literary work without being given any specific guidance, but the great thing about this type of assignment is that it allows you to focus on an element of the poem that interests you. As the question suggests, you will need to make a "point," or argument, which means that you will need to, first, identify a theme or point of interest, and then consider what thesis statement you would like to make drawing from that starting point.
Some good themes for essays on this poem might be:
- the idea of kingship according to the Anglo-Saxons, and how this is expressed by the various kings in the poem;
- the idea of womanhood in Anglo-Saxon society, and how the various female characters in the poem represent the different ways to be a good, or bad, woman within that society;
- pride in the poem, and how far this constitutes Beowulf's "fatal flaw";
- the digressions in the poem, why these were chosen, and what they lend to the main narrative;
- the key battles in the poem and what these evils represent.
There are others you may be able to think of yourself.
Let's take one of these as an example of how to formulate, and support, an argument using quotations from the text. Let's say we want to argue the following:
"One of the key themes of Beowulf is kingship according to the Anglo-Saxon model, and how a good king should face and overcome his challenges."
That's our position. To support this position, we first need to expand on it a little more:
We know this is important to the poet, because the very first characters he describes are some of the earlier kings of the Danes, with reference to their "ellen fremedon," or courageous deeds (line 3). In line 11, the poet explicitly describes Scyld Scefing, who forced the bordering tribes to submit to him, as a great king: "þæt wæs gód cyning."
We've now set our scene, and we've supported it with quotations from the text. We might then move on to say:
1. The two key models of kingship in the text are Beowulf and Hrothgar.
2. Hrothgar, like Scyld, is described as "gód cyning" (a good king) (line 863), being gracious and worthy. However, he is at a different point in his life than Beowulf—he is now an older man, and it is clear from the text that it is not frowned upon for him to ask someone stronger to come and defend his people. Hrothgar is still fulfilling his role in defending his people by inviting in another person, a renowned warrior, to tackle an evil.
3. Later in the text, we see Beowulf in the time of his own kingship. He performs kingship as an old man in a different way than Hrothgar; he dies for his people. Note, however, that he does not leave them in chaos or unprovided for—you could take quotations from the famous "hero on the beach" sequence, in Beowulf he talks to Wiglaf about who should succeed him, for evidence of this.
You may, of course, choose to focus on something other than kingship in the poem, but hopefully this gives you an idea of how to proceed.