First of all, you should have a sound knowledge of history. Most of the times, the literary critics work under the influence of historic events. They look at things in the context of history and evaluate the literary work while having past events and characters in mind.
For instance, if you are reading a criticism on a war novel of Greek times then the critic would have raised questions or praised the author in the light of that era. You cannot understand him until you have a sound knowledge of that time period.
Equip yourself with philosophy:
Studying philosophy is also very important to understand the literary criticism. The reason is that the fundamentals of criticism were given by two philosophers Plato and Aristotle. The former asserted that art should be judged on the basis of objectivity whereas the latter believed that the art should be evaluated just on the basis of creativity. These two approaches will help you in understanding the mind of critic.
Understand the psychology:
You must know what affects or impacts literature leaves on the reader. This will be really helpful for you to peep into the mind of critic. Understanding the psychology of human beings can enable you to read between the lines and ultimately nothing will be difficult for you in literary criticism.
Read literary criticism as a piece of literature:
Another technique to understand the literary criticism is to read that article as an independent piece of literature. Criticism is sometimes free of all the influences and simply focuses on the content, type and language.
Get the political information of that period:
Last but not the least; you should get the information about that period in which that literary criticism was done. Social, political and biographical conditions always have great influences so you must not talk down these factors.