Reader-Response Criticism is about interpreting a piece of literature not solely on the merits of the piece of literature but rather as an interaction between the reader and the piece of literature. The reader's reaction, how the piece affects the reader, is taken into consideration when interpreting a piece. Essentially what this theory means is that the text itself has meaning and the interaction between the reader and the text also carries meaning. The interpretation in Reader-Response Criticism lies between the intersection of these two sets of meaning when evaluating a text.
Post-Colonial Criticism examines works written by colonial powers and its subjects. Post-Colonial Criticism considers many lenses through which to evaluate a piece---including politics, power, culture, language and religion. A seminal piece often used in teaching this theory is Chinua Achebe's "Things Fall Apart," about his native Nigeria's experience of colonialism. This theory fleshes out what it means to be colonized on a social level, and even more closely, on an individual level, exploring how colonialism shapes and affects identity.
For New Historicists, a piece of literature is shaped by the time period in which it was written and thus must be examined and interpreted in the context of that time period. This theory attempts to tie the characters, events and language in a piece of literature to events from the time period in which it was written. It also looks at mainstream and marginalized populations as well as traditional and subversive discourses of the era when interpreting a text. New Historicists also take into consideration political and cultural events that the author lived through. All of these various pieces, along with the time period the piece of literature is set in, are part of the interpretation process for New Historicists.
Feminist Criticism analyzes text through the lens of how women have historically been portrayed in literature. It examines the political, social and economic subjugation of women in society. It further looks at how the characters, the dialogue, the events and resolution of a piece of literature can serve to either reinforce or challenge stereotypical representations of women.
Deconstruction Theory is about shifting the center of a piece from the author outward, to the reader and the piece's deeper meaning for society. It removes the author as the authoritative voice on a piece to those reading and interpreting the piece. In this vein, it has much in common with Reader-Response Criticism. Where this theory differs from other theories is that it looks at a very unique aspect of a text---it analyzes what was left out of a text and how that influences the piece as much as what was actually written into a piece.