Writing in the mode of Postmodernism typically focuses on the identity of the individual. A lot of the basis of the philosophy works off of the tenants of Existentialism, in which the individual maintains agency in their will. Where Postmodernism deviates from this tradition is by stressing the transience of the individual. Every day the individual wakes, they wake as a new person. What we are one day is not true of the next. Were you to ask me why I wrote about Existentialism a week or so ago, I would answer as a Postmodern, "That day who I was thought it would be a good idea." So, to a certain degree, Postmodernism is about destroying the notion of the static individual. Instead we are the sum of our experiences. This is why most ad campaigns follow a particular formulaic approach of blasting folk guitar music with esoteric percussion instruments in car commercials. The idea here is that when you buy the car you are not buying a vehicle designed to take you to and from work. Instead, it is a consumer experience that is being purchased. Apple Inc is guilty of this marketing ploy. Watch any of their commercials and you will see that they are marketing experiences and not gadgets.
Another aspect of Postmodernism to consider is that the philosophy of writing changes. Just like the individual, Postmodernism also deconstructs the methodology of writing. Early examples of this can be seen in stream of consciousness prose in Joyce's Ulysses. Additionally, Grant Morrison's early works in comics break down the traditional expectations of comic narrative in like manner, often taking a non-linear approach to story. Employing these methods in writing serves the purpose of expressing emotion or plot in a novel way. Joyce would write sentences that would run all together to create a sense of urgency in the character, or Morrison would take a panel and thread throughout the imagery an entire copy of his original script that he gave to the editor and illustrator to emphasize metaphysical self-awareness. Beyond that, much of Postmodernism in writing will just intentionally deviate from the perceived structure of earlier forms. There are so many varieties in this that cataloging the tropes and forms is nearly impossible.
Here's an Example:
Transcendent beats. Tribal pulses. I am lost in the mire of sound. Sweat and spittle permeate the air that suffocates me. The Shaman that spins the sun pounds life into my soul as the rave ebbs and flows through my consciousness. No longer am I myself. I am the waves of light that feed the mists. Feel my arms. Take them in your breast. Envelop them like a child in the womb. Trails and afterimages surround the skyline. Ants and beasts, burdened with insignificant purpose cling to civilization. I am one with the earth, ground to dust by the bass.
"You want some E? Fuckin' rip your mind out, man!"
Who are you, apothecary? Drugs alter the mind, but not the soul. I am freed from my slavery in them. She smiles like a Cheshire cat. In the plum haze her teeth are bleached as bones. She is a lie. What are you?
"Gimmie!" The words tumble out, limping.
By the masses my soul is compressed to a singularity. I am no longer man, woman, or beast. I am one with the shaman. Nirvana takes me and I am no more.
This is difficult to categorize, but here you can see that the narrator dancing in the club is a victim of the Postmodern spirit. Lost in a sea of ambient soundscapes individualism is lost on the subject. As with most psychotropic experiences the goal of the user is to escape their own awareness of self and become one with their environment. I would suggest that this is reactionary to the spirit of Modernism which attempted to create a utopia for absolute truth. When this Enlightenment agenda failed, everything that was considered given as truth went out the window, including the essence of the individual. It is this spirit that Postmodern literature attempts to emulate. How this philosophy melds with writing then is made a little more clear, but my greatest suggestion is to consider what you are writing and why you are writing it when using this style. It is possible to just crap something out that doesn't mean anything so I recommend employing discretion in your stylistic choices.