Right off of Wikipedia:
Theory
Derrida began speaking and writing publicly at a time when the French intellectual scene was experiencing an increasing rift between what could broadly be called "phenomenological" and "structural" approaches to understanding individual and collective life. For those with a more phenomenological bent the goal was to understand experience by comprehending and describing its genesis, the process of its emergence from an origin or event. For the structuralists, this was precisely the false problem, and the "depth" of experience could in fact only be an effect of structures which are not themselves experiential. It is in this context that in 1959 Derrida asks the question: Must not structure have a genesis, and must not the origin, the point of genesis, be already structured, in order to be the genesis of something?[3]
In other words, every structural or "synchronic" phenomenon has a history, and the structure cannot be understood without understanding its genesis.[4] At the same time, in order that there be movement, or potential, the origin cannot be some pure unity or simplicity, but must already be articulated-complex-such that from it a "diachronic" process can emerge. This originary complexity must not be understood as an original positing, but more like a default of origin, which Derrida refers to as iterability, inscription, or textuality.[5] It is this thought of originary complexity, rather than original purity, which destabilises the thought of both genesis and structure, that sets Derrida's work in motion, and from which derive all of its terms, including deconstruction.[6]
Derrida's method consisted in demonstrating all the forms and varieties of this originary complexity, and their multiple consequences in many fields. His way of achieving this was by conducting thorough, careful, sensitive, and yet transformational readings of philosophical and literary texts, with an ear to what in those texts runs counter
Straight from the words of Derrida in an interview.
Came across this quote which does a good job of describing a deconstructionist approach:
Derrida says, "There is the general structure of Messianicity as the structure of experience, and on this groundless ground there have been revelations, a history which one calls Judaism or Christianity and so on. That is a possibility and then you would have a Heideggerian gesture, in style. You would have to go back from these religions to the fundamental ontological conditions of possibilities of religions, to describe the structure of messianicity on the groundless ground on which religions have been made possible (23)".