Bob Dylan's song combines the romantic and the political quite beautifully. The two strands complement each other in the song. In these lines, Dylan comes back to the central question of what does it take to be human, which he keeps repeating in different forms throughout the song. He examines the values of human experience, the limits to human tolerance, indifference and habituality, before it all breaks free in the revolutionary upsurge--" How many years will it take till we know/That too many people have died".
These questions are rather unanswerable and the answer will always be blowing in the wind. In the lines quoted in the question, Dylan questions the onset of intuition, sensibility and awareness in temporal terms. How many occasions does a man need to arouse his sense of insight into his own social responsibility. However, at a more individual level, the lines may also refer to the timing of epiphanic knowledge. The following lines make the sense clear--"How many years must one man have/Before he can feel, he can cry". This is a clarion-call to man's waning sensibility at the wake of social disasters.
I believe the statement "How many times must a man look up before he can see the sky," is referring to man's inability to see that which is right in front of him. Quite often people go through life complaining about the little thing going on in their lives, but they forget to look at what they do have in their lives. For example, a person who always complains that his son never does anything around the house, but does not notice that his son takes out the trash, comforts his little sister an lets her tag along, etc.
Man has a tendency to forget what he has. In this statment it is a metaphor for the things in man's life that he ofte over looks. They have always been there for him to embrace but he doesn't notice them.