Postmodernism refers to a period in history (roughly 1945-present) and also an artistic movement with particular themes and styles. Postmodernism is a reaction against Modernist themes and philosophies. Postmodernists are particularly skeptical of what Jean-Francois Lyotard called "grand narratives." A grand narrative is a complete, totalizing system of thought and practice. Some examples are Communism, Capitalism, Industrialization. Grand narratives can also be artistic movements such as Futurism or the Avante-garde. They can also be political as well as theological. Lyotard raged against grand narratives because he thought that unifying a world under one way of life was always done so through violence (colonialism, Nazis, failed communist states, imperialism, exploitation under capitalism). Also, and this speaks more to the arts and meaning in everyday experience, uniting the world or nation (in the guise of progress) by enforcing a singular way of living eliminates difference, variety, and diversity. Therefore, postmodern theorists have tended to favor more diversity, plurality, and local (rather than grand or national) differences.
Deconstruction is a philosophy related to this postmodern critique of totalizing systems of thought because deconstruction is the practice of exposing the flaws in such systems, particularly in the binary oppositions (public/private, man/woman, etc.) that inform those systems.
It's hard to say what the postmodern project is "in general" because postmodernism is a practice of avoiding generalizations. But, for the sake of trying to answer the question, the postmodern project is based on skepticism of truth, questioning and tinkering with art and knowledge of the past, a celebration of diversity, and a challenge to all manifestations of authority.
Toni Morrison's Belovedis postmodern because it avoids a totalizing narrative authority (narrator), because fiction and history are intertwined to a point that truth becomes interpretation, and this is therefore a postmodern tinkering (bricolage) of history and the notion of history as being true. This is a good example of the postmodern skepticism of grand narratives and deconstructing those narratives and other so-called authoritative versions of history.
In light of all these postmodern motivations, postmodern authors would also experiment with the method of writing itself. Multiple narrators, non-linear progressions, and intertextuality were methods used to disrupt the traditional flow of literature in order that the reader would slow down and consider the construction of what he/she was reading (just as postmodern theorists wanted to consider the construction of histories and truths they were given to believe.) Because postmodern writers challenged all manifestations of totalizing truth, postmodern literature is often characterized by uncertainty and lack of closure, both of which prompts further thinking on the part of the reader.