Deconstruction is a way to interpret and critique a piece of literary art. You literally deconstruct the meaning behind the piece and break it down as much as possible via the language and imagery used by the author... It came about because of Jacques Derrida, a French philosopher who is simply amazing but it can be difficult to grasp and quite formidable because it's based on the ideas of linguistics... For Derrida, all communication (especially writing) uses signs (letters, numbers) which yield more signs (words, which yield sentences, which yield paragraphs, which yield stories).
Also, deconstruction is really difficult to define, as it is believed that Derrida would never have wanted it to become a way to pick apart or criticize literature. He would never define it, but rather, define what it is NOT.
http://en.wikipedia.org/wiki/Deconstruction <--- Wiki page that will help a lot.
I found the easiest way to deconstruct a piece was to pick out the Binary Oppositions within a piece - the two conceptual oppositions (God/Humans, Good/Evil, Up/Down, etc.). Like, we know there is truth, because we have been deceived - without deception there would be no truth... we know good because we have experienced bad,... etc. etc. etc.
http://www.cobussen.com/proefschrif...cal_oppositions/hierarchical_oppositions.html
Check out that essay on Binary Opposition, which to me is the easiest of the strategies of Deconstruction.
Which essay were you asked to Deconstruct? When is it due? I LOVE Literary Criticism and once you realize HOW to see the meaning of a piece, you'll never read something without realizing the meaning again...
And don't be nervous - this is a difficult theory and heavy on philosophy so your instructor is probably anticipating a lot of questions and confusion,... in fact he/she probably WANTS to see how confused you'll get - it's probably part of the lesson.