God
The idea of a personal God is Nietzsche's primary consideration in these writings. He isn't writing from a religious point of view. That is to say, Nietzsche is comfortable explaining away certain religions first, and then dealing with the remaining possibility that perhaps God exists and religions are wrong. He writes through lengthy meditations about his beliefs, and he explains that if there is a God, what that might mean about reality to him, and he explains why he comes to the conclusion that perhaps there was once a God, but now, "God is dead."
The madman
There comes a point in his writings when Nietzsche explains through parable what his life is like. He identifies himself as a madman in a village who comes into town carrying a candle. The town is full of atheists, and so he should fit right in, but instead, the town asks him, "Why are you carrying a candle?" and Nietzsche's madman explains that if one believes there is no God, they should not trust the reality that they observe by the light of the sun, because true atheism doesn't trust the sun either. The metaphor is that to say there is no God is like saying there is no sun, and although he says it, he comments that the vast majority of atheists still live as if life has meaning, as if there is a God.
The thinker
The reader is urged to become this character, a person who frees their mind from the social constructs that constrain it. The thinker is a person who reaches the conclusion that the truth is worthy of pursuit, even at the expense of social company. This person is someone who is willing to step out past shame into the possibilities that life might show to him through his mind. The issue is famously controversial, so Nietzsche's "thinker" will be someone comfortable with controversy.
