If the interested party is already well read in the philosophical works of Husserl, Heidegger, Hegel, Nietzsche, Freud and Levinas, I could probably do it in a weekend.
(Or as Chomsky argues - why is deconstruction necessary when the conclusions it reaches can be simply divined by ordinary laypersons, without all the verbosity and the pretentiousness of language?)
Let's start with you reading (and demonstrating to me a core competence of) the basic texts of philosophy leading up to deconstruction-- in this case, that would be Husserl, Heidegger, Hegel, Nietzsche, Freud and Levinas.
When you have those six down, I'd be happy to explain deconstruction to you.
What you should be saying is "Deconstruction is an approach, introduced by French philosopher Jacques Derrida, which rigorously pursues the meaning of a text to the point of exposing the contradictions and internal oppositions upon which it is apparently founded and showing that those foundations are irreducibly complex, unstable or impossible" (courtesy wikipedia).
And then the layman asks "how does this approach expose contradictions?"
And you say "Deconstructions work entirely within the studied text to expose and undermine the frame of reference, assumptions, and ideological underpinnings of the text. Although deconstructions can be developed using different methods and techniques, the process typically involves demonstrating the multiple possible readings of a text and their resulting internal conflicts, and undermining binary oppositions (e.g. masculine/feminine, old/new)."
and there we have it, good enough for the layman to realize it's a line of thinking he's probably not interested in pursuing anymore. And then...if they keep on that, you say, "this is getting a bit into the deep end for me to make it simple and explainable, if you are really interested, start by reading these books first."