"The Wife's Lament" is an elegiac and lyrical poem typically found in the Anglo-Saxon period (although it was created in Greece). Poetry from this period contained many specific literary devices and characteristics from the period.
An elegiac poem is constructed in three parts. The first part of the elegiac poem presents the speaker's lament (grief over the loos of a loved one). Next, the speaker praises the life of the deceased. Finally, the speaker finds consolation (many times in the belief of God-- as in "The Seafarer" and "The Wanderer").
Outside of the elegiac features, many poems from this period included the use of kennings and alliteration. A kenning is a, often, hyphenated word used to elevate and beautify the language of the poem. For example, a kenning for ocean is whale-path, and a kenning for blood is battle-sweat (as seen in Beowulf).
Alliteration is the repetition of a consonant sound within a line of poetry. An example of alliteration found in "The Wife's Lament" is as follows.
I make this song of myself, deeply sorrowing.
In this initial line, alliteration is found twice. Both the "m" in "make"/ "myself" and the "s" in "song"/ "sorrowing" denote alliteration.
Lastly, the poem needs to contain elevated language. Elevated language is formal and includes the inclusion of elaborate speech (done through using both kennings and alliteration). Following the characteristics defined above will help you in creating a version of "The Wife's Lament."