They used predetermined launch and flight paths made on earth, or relayed information from Mission Control. Just because the lunar module had no processing power doesn't mean that the rocket it was on was unable to get to the moon, especially since the lunar module didn't actually control much, if anything, on the rocket itself.
And you are trying to prove something. You're trying to prove that because this cell phone exists, there's no reasonable way astronauts were able to go to the moon in the technology available. Which is such a major logical fallacy I don't even know where to begin on that point.
