For postmodern philosophy, it is suggested to read (or at least be familiar with) the major works of (in no particular order) Martin Heidegger, Friedrich Nietzsche, Gilles Deleuze, Maurice Blanchot, Jacques Lacan, Jacques Derrida, Michel Foucault, Jean Baudrillard, Slvaoj Zizek, Alain Badiou, and Gianni Vattimo. To a lesser extent, knowledge of previous major philosophers (Plato, Aristotle, Descartes, Hume, Kant, Hegel, Kierkegaard) is also a bonus.
With regard to theology, a good knowledge of historical theologians such as Karl Barth, Augustine, Thomas Aquinas, John Duns Scotus, Paul, John Calvin, Paul Tillich and more contemporary theologians such as Thomas Morris, Alvin Plantinga, C.S. Lewis, Dietrich Bonhoeffer will be a good basis.
Additional knowledge of Geza Vermes, Brian McLaren, Stanley Grenz, Stanley Hauerwas, Ludwig Wittgenstein, Blaise Pascal, and others will also be helpful in the conversation.
The picture there is the first non-human picture from Google Images for "Postmodern Theology"...