Postmodernism (while including the already mentioned aspects of relativism and deconstructionism) is also characterized by suspicion and skepticism of anything classified as "modern," which means really anyone/thing which makes claims of over-arcing objectivity or certainty regarding truth, which are seen as "power plays," an attempt at controlling the thoughts and behaviors of others, which is one of the few things viewed as (dare I say, absolutely?) immoral from within the framework.
The Tower of Babel has been used as a helpful metaphor: It's as if modernism built a prideful tower of so-called truth, certainty and knowledge on an unbiblical foundation ("Look at what modern man has accomplished"), and postmodern deconstructionism results from God confusing the language. As Gene Veith put it, "Modernists did not believe the Bible is true. Postmodernists have cast out the category of truth altogether. In doing so, they have opened up a Pandora's box of New Age religions, syncretism, and moral chaos."
If you're interested and you've got the time, D.A. Carson's book
The Gagging of God is probably the best treatment of the subject, of which I'm aware (it's the best treatment of many subjects, In my humble opinion). Gene Veith's book
Postmodern Times is also useful, and shorter (it's where I got the above quote). I'd also recommend the David Wells trilogy. A compilation book called
Telling the Truth edited by Carson might also be helpful, since you could pick and choose which chapters sound helpful and interesting or not.
Or, if you don't feel like reading, the Desiring God National Conference '06 DVDs on
The Supremacy of Christ in a Postmodern World are fantastic:
The Supremacy of Christ in a Postmodern World :: Desiring God