I assume that you're asking more specifically about the relation that "postmodernity" and "poststructuralism" might have to historiography and the practice of history, rather than in philosophy or literary theory. I'll begin first by bracketing out "postmodernism," which is a notoriously slippery term described both as a state of culture (see Jameson, which every undergrad has to read at least once) and also a mode of philosophical thought. When discussing these terms, I find it's pretty common to get into minor quibbles about who "counts" as one or the other, which is not that helpful - so I'll stick with post-structuralism, which doesn't also potentially refer to art, literature, or architecture.

For my purposes here, I'm going to focus on a general description of Michel Foucault's historiography, which hopefully I won't mess up too much.^1 Foucault was something of a philosopher / historian hybrid, and his work has influenced the ways that historians understand the mechanisms of historical change and the intertwining of knowledge and power. For Foucault, knowing isn't just half the battle - it's the whole damn thing. People's identities are not somehow intrinsic or inborn, but are instead the result of the operations of power and knowledge that render certain aspects of those people legible.

That last sentence probably read like word salad if you're not familiar with Foucauldian scholarship. To give a more concrete example, think about depression as a mental illness. Today, there exists a great deal of knowledge about depression - we have codified its symptoms, prescribed pharmacological solutions, teach its treatment in institutions, and many more things that I've not mentioned. But did people "have depression" in, say, turn-of-the-century America?

It's tempting to say yes - to universalize what we call "depression" as somehow inherent or natural to the human experience. But Foucault would say no. "Depression," for the Foucauldian scholar, only makes sense within a cultural and historical context that actually produces its meaning, labels and categorizes people with it, and creates spaces and institutions that contain and control it.

So is Foucault saying that people didn't feel sad before the DSM identified and codified "depression?" No, this is not what Foucault is saying. Instead, he's suggesting that different historical moments define mental illness differently, and that the task of the historian is to try to describe how forms of knowledge (science, medicine, law, etc) produce those categories of illness themselves.

Within this framework, the notions of "experience" and "truth" suddenly become destabilized. If, as Foucault suggests, subjects are produced by the operations of power and knowledge, then accounts of "experience" are by necessity filtered through those operations. In other words, primary source documents do not provide a clear "window" with which to "see" the past, because the experiences codified in those documents are already filled with a bunch of tacit assumptions!

OK, so now we're finally able to address your question about "truth" in relation to Foucauldian historiography. If subjects do not exist "naturally," but are instead produced through the intersections of a bunch of larger institutions and discourses, then their experiences are not objective accounts of some sort of external reality. So, when we write history, we can't really reproduce a picture of the world as people in the past experienced it, and we can't really make people in the past "speak" - instead, we investigate the terms of possibility that made that speech possible, legible, and interpretable in the first place.

Anyway, this is a long and complex question that causes all graduate students to break into a cold sweat at the thought of having to explain it, as I myself am currently doing. Others might be able to chime in and refine the above, or to disagree.

^1 I'm being reductive here - there are ton of scholars and philosophers who are important. Understanding what "structuralism" is, for instance, is critical to conceptualizing what "post-structuralism is. Derrida is also critical both for the way in which sources are read and how the archive is understood, but I think this is also confusing. I don't mind expanding here, but these are longer, other posts.

This is probably better suited to somewhere like /r/askphilosophy.

There was a Monday Methods feature a couple of weeks ago on Post-Modernism in academia. You may find some of the responses there helpful.