Modernism is very much from the print era with its hierarchical, rational, centered, and scientific structure. It's from the democratic era of print in which authors used deductive theses to prove their claims. It seems to be mostly about ideas (abstract), presented in a cause-effect organizational plan. Also, modernism is based in Western (European/American mainly) values and culture (again, mainly democracy and capitalism).
Postmodernism, by contrast, is from the current mass media (TV, computer) era and, therefore, more random, multicultural, subjective, and populist--in other words, there's no top-down hierarchical structure. Postmodernism wants to include all, namely feminist and minority culture that have been excluded from the modernist past. Also, postmodernism largely rejects Western values and culture, looking at more diverse, complex, and associative (not cause-effect) systems of organization, cultures, and beliefs.
Good examples of these dichotomies can be found in novels about war. Whereas a modernist war novel may be a first-person point of view which shows the horrors of war on a few individuals (through Western eyes), very much like All Quiet on the Western Front (1929), a postmodernist war novel like The Things They Carried (1990) switches narrative POV, setting (time/place), and themes (non-Western) in order to show the chaos of war, as well as the problems with memory and point-of-view. O'Brien very much focuses on the roles of women ("Sweetheart of the Song Tra Bong") and the feelings of the Vietnamese (enemy), even devoting a chapter to an unknown "Man I Killed."