Disclaimer: This is a really brief, over-simplified, slightly biased guide to some literary theories. Reading this does not give you the right to be pretentious; it just means you will be less confused when other people are being pretentious.
According to Liberal Humanism, certain texts are part of the canon, or The Ultimate List of the Best Things Ever Written. It’s the job of a literary critic to look at the themes and ideas in texts that are part of the canon. If that sounds like a really vague theory, that’s because it is.
Formalists and New Critics are people who got fed up of the vagueness of Liberal Humanism. They decided that literature should become more scientific, so they set about studying literary devices (metaphor, alliteration etc.) and how they made literary language different from ordinary speech.
No, you don’t have to be a Communist to use this theory; but you do have to believe that all literature is political, even if the writer doesn’t want it be. Critics who use this theory tend to focus on the political ideas in the text: what they are, why they are there, and how they are put across.
Structuralists believe our world is full of signs and systems that don’t exist naturally, but because we create them and give them meaning. You can’t pay your rent by writing a note that says the bank will pay up if the landlord asks, but you can use a cheque, which is essentially the same thing. When looking at a piece of writing, Structuralists look at the signs and patterns in the text to figure out how it works.
Post-structuralists take Structuralism one step further. If signs only have value because we say they do, then why should we pay so much attention to them and let them control the way we think and behave? So, they don’t look at the stuff in the text that follows the rules, but the points where it all breaks down and exposes the arbitrariness of those ideas.
Having or being part of an empire is going to affect how you think about yourself and other people in that empire. If the empire breaks down, you have to forge a new identity and a new set of relationships. Post-colonialism looks at all of these different things affect literature. There tends to be a racial aspect to this kind of analysis, and Star Wars puns. No, really, The Empire Writes Back is a thing.
Feminism is a fairly self-explanatory one; it’s closely related to the political ideas of the feminist movement. This theory can be divided into 2 branches: Anglo-American and French. The Anglo-American side of things look at the socio-political aspect of writing for, about, or by women. The French school is linked to Post-structuralism and looks at how language and gender interact.