How should one read Beowulf?

I would always strongly recommend reading Beowulf in the original Anglo-Saxon. There are many very good translations of Beowulf, but by necessity these use artistic license and do not always give us the best idea of what is specifically being said by the original poet. You also miss out on the beauty of the language and the impact of the alliteration to give cohesion to the poem if you read it in translation.
Many texts of Beowulf will come as a "facing page" translation—that is, with the Anglo-Saxon on one side and the English mirroring it on the other side. Anglo-Saxon can seem extremely confusing at first, but most copies of the poem will come with a glossary for the more obscure words, and if you get stuck, you can always look at the modern English for help. You will find that once you get going, you start to make sense of the Anglo-Saxon on your own. Reading Beowulf armed with a translation, then, is an excellent way to start out in learning and appreciating Anglo-Saxon properly. You can also find a very good translation of this kind online for free—see my link below.
If you'd like to know how the Anglo-Saxon is supposed to be said, there are lots of resources online to help you with this, too. Please see my link here. As a general guideline, remember that "c" is always hard, unless followed by an "i" (so "cyning", modern English king, is pronounced "kinning," while "cild," modern English child is pronounced "chilled.") The ae sound is pronounced like the a in "cat," and sc is akin to modern "sh." You'll also encounter some special characters, thorn and eth, which are both pronounced as "th."
http://www.heorot.dk/beowulf-rede-text.html

There is much alliteration in the poem ("Alliteration" is a literary technique in which the first letter or the initial sound of a word is repeated.")
Examples:
"the Wielder of Wonder, with world’s renown..."
"while wielded words the winsome Scyld..."
"No less these loaded the lordly gifts..."
There are four feet per line in Beowulf. A poetic "foot" is a repeated sequence of meter composed of two or more accented or unaccented syllables. There are four beats per foot (i.e., a poem's rhythm).
Beowulf should be read with a pause between the second and forth beats. This literary device is called a "caesura."