Derrida's works are very difficult to read. You don't stand much of a chance without some background in Kant, Hegel, Husserl and Heidegger. The most readable accounts of his ideas for the layman are in the interviews he gave, where he was forced to simplify. I recommend "Points" and "Positions'. I also recommend encapsulations of his ideas by other authors. My favorites are "Tain of the Mirror" by Rodolph Gasche, and "Derrida' by Geoffrey Bennington.

Here's some basic quotes from Derrida concerning his core notion of differance:

Derrida writes, "...an element functions and signifies, takes on or conveys meaning, only by referring to another past or future element in an economy of traces"(P29). He adds:

"The play of differences supposes, in effect, syntheses and referrals which forbid at any moment, or in any sense, that a simple element be present in and of itself, referring only to itself(P26)"

"The iterability of an element divides its own identity a priori, even without taking into account that this
identity can only determine or delimit itself through differential relations to other elements and hence that it bears the mark of this difference. It is because this iterability is differential, within each individual
"element" as well as between "elements", because it splits each element while constituting it, because it marks it with an articulatory break, that the remainder, although indispensable, is never that of a full or
fulfilling presence; it is a differential structure escaping the logic of presence..(LI53)."

"[This] iterability alters...leaves us no room but to mean (to say) something that is (already, always, also) other than what we mean (to say) (1988,p.61)... It is not necessary to imagine the death of the sender or of the receiver, to put the shopping list in one's pocket, or even to raise the pen above the paper in order to interrupt oneself for a moment. The break intervenes from the moment that there is a mark, at once. It is iterability itself, ..passing between the re- of the repeated and the re- of the repeating, traversing and transforming repetition(1988,p.53)."

Thanks very much Joshs. I totally agree with you that one needs some background in order to understand Derrida. I have tried to understand Derrida through his critique of Saussure as I know Saussure's semiotics very well.
with regards to relationship between reality and representation, 1) Derrida does not deny the relationship between reality and representation. This can be inferred from the quote "It is totally false to suggest that deconstruction is a suspension of reference" (Derrida 1984, pp. 123-124). Of course, the reference here should be understood as slippery and indeterminate reference given differing and deferral rather than a simple and transparent reference.
There are other related questions. Say, what does Derrida say about reality? I mean what is his ontological view?

Derrida's works are very difficult to read. — Joshs

Ain't that the truth! Is it not a criticism of metaphysics? Something like an argument for the impossibility of ye old metaphysical dream? And yet one seemingly has to be steeped in the same culture that is being undermined to appreciate it?

Correct me if I'm wrong, but is this not justified in terms of metaphysics lurking everywhere? So we have to be steeped in metaphysics in order to avoid or transcend metaphysics?

Derrida's argument is not that we transcend metaphysics and not that we're stuck in it, but that we perform a kind of dual move in moving through experience. New experience must carry forward the past in order to be recognized at all. This is the metaphysical gesture(repetition of the past as idealization). At the same time, repeating experience exposes it necessarily to contamination by new context. This is the empirical gesture. So Derrida calls this binary structuration of all experience as simultaneously formal and empirical, simultaneously an inside and an outside, the quasi-transcendental.

New experience must carry forward the past in order to be recognized at all. This is the metaphysical gesture(repetition of the past as idealization). At the same time, repeating experience exposes it necessarily to contamination by new context. This is the empirical gesture. So Derrida calls this binary structuration of all experience as simultaneously formal and empirical, simultaneously an inside and an outside, the quasi-transcendental. — Joshs

That rings true. Out of curiosity, does he ever say it as well as you just did? (This reminds me of James' pragmatism, by the way. The past collides with the present.)

The thing about getting Derrida is that you find yourself recognizing what others miss about the way we use language. Heidegger was the first philosopher to put 'is' into question, the way we use 'is' between a subject and predicate to build a description of the world without asking what is presupposed by doing this.
Derrida makes us rethink every opposition we articulate(past colliding with present) in order to uncover the way in which each term already is complicated or divided within itself, even before we can oppose it to something else. Even the word 'difference' he rethinks by spelling it 'differance', to demonstrate how a meaning both differs form another and defers that difference.

Is that you, tED? It seems like déjà vue, all over again.

‘No metaphysics’ is a kind of metaphysics; the worst kind, as it usually works out.

Derrida makes us rethink every opposition we articulate(past colliding with present) in order to uncover the way in which each term already is complicated or divided within itself, even before we can oppose it to something else. — Joshs

I can relate to this thought especially. I had a go with Wittgenstein once and that led me to see how messy and tortured meaning is in the claws of philosophers. They rip words out of context. They pin down the butterfly at the cost of its life.

Heidegger was the first philosopher to put 'is' into question, the way we use 'is' between a subject and predicate to build a description of the world without asking what is presupposed by doing this. — Joshs

I relate here, too. At the moment, I'm tempting to aim at the gap between theory and life. The world is 'really' X usually has little to do with how live is lived away from such statements. Someone around here used the word 'theology.' That gets the feel right. Lots of philosophy is a kind of theology of Truth, it seems to me. 'Theology' captures its artificiality.

I don't see how we could know one another. But my views do strike me as pretty generic, so someone has surely run through these permutations before. With a name like Theo, you might think I'd be more theoretical.

‘No metaphysics’ is a kind of metaphysics; the worst kind, as it usually works out. — Wayfarer

Perhaps. I don't know. I find it hard to finish most philosophy books. I have a friend who reads the big shots and he gives me impressive paraphrases. But I also wonder how much of that is him and how much was already there in book. He gave me the run-down on Hegel that I saw elsewhere. It was the same story of God really being the dude that looks for God. It seemed like a thinking man's kind of religion to me at the time. Especially around that fire passing the bottle back and forth.

Derrida was always clear that we could never 'escape' metaphysics, and that any attempt to do so would be all the more metaphysical for it. He definitely did not disavow metaphysics, as least not in any straight-forward way.

As for an ontology, the question is alot harder: it's perhaps more fair to say that Derrida sought to think the conditions of possibility of any possible ontology. Whether or not those conditions themselves resolved into any particular ontology is not quite an appropriate question I think - Derrida always struck me as a formalist and any attempt to draw 'an' ontology out of his work would seemed to be doomed to failure.