You will write your literary criticism analysis from the perspective of a particular theory of literary criticism. There are many major theories that you have to choose from. To explore the possibilities, read this guide from Purdue University's Online Writing Lab.
Your first task is to develop keywords, which you can think of as search terms to use in the library databases listed below. That will, fortunately, be extremely easy for this assignment. Searching for the title of your work, such as "Beowulf", should be sufficient.
For this annotated bibliography assignment, you will need to search two databases. If you are using the library databases off campus, then I suggest that you first watch this video explaining how to access the databases off campus.
The video embedded above shows you how to search Academic Search Complete, which is an excellent source of information for literary criticism.
Remember to limit your search results to scholarly (peer-reviewed) journals. This is an essential step.
JSTOR is a database of scholarly journals in the arts, the humanities, and the social sciences. It contains many works of literary criticism. The above video shows you how to search it.
When you set up your own search, remember to limit your item type to "Articles".