Phenomenology is a kind of method you can adopt for reaching conclusions: introspecting your experience to reveal various wider-&-deeper surprising-or-distressing things. Husserl recommends introspecting your ideas to reach certainty about how things must be. Heidegger recommends attending instead to your skills and moods, and Sartre to your emotions, imagination, and ego, to reach their existentialist conclusions below. Nietzsche (born posthumously) is an opponent of this method, dissing introspection as uncertain about oneself and unrevealing beyond.
Existentialism is a kind of conclusion you can reach: that you are surprisingly-or-distressingly free from various wide-&-deep aims/duties/rules/ruts. Kierkegaard concludes you're free from objective ethical and epistemic duties. From their phenomenological method above, Heidegger concludes you can be free from mental rules and social ruts, and Sartre concludes your will is free from objective ethical duties. de Beauvoir concludes you can be free from gender ruts and men's rule. Nietzsche is a frenemy of such conclusions, subjecting everyone to objective ethical duties (though these differ according to one's power), and (half-)dissing both freedom and women.
After we briefly introduce their precursors (Kant, Hegel, Schopenhauer, Marx), we'll act as if the phenomenologists and existentialists are all in a café, discussing specific topics and trying to fend off Nietzsche.