How did newton discover the law of universal gravitation?

He turned off his smartphone, his TV, his mp3 player, and his Gameboy.
He told his housekeeper that he didn't want to be disturbed, and then he
went into his room.  He sat down with an ink pen and his notebook, and
he started thinking.  He thought and thought and thought, about all the
things he had seen, and all the things he had read in books, and in letters
from his friends who were thinking about the same things that he was.
He wrote down a lot of ideas.  Some of them didn't work out when he
thought about them some more, and others looked better. 

After a long while of thinking, he had formulas that he thought might be the
answer.  But before he could tell everyone else about them, he had to test
them, to see if they would actually work.  He decided to test his formulas
of gravity with the motion of the planets around the sun.  There was a lot of
excellent data on exactly how the planets move, and a fellow named Kepler
had worked with that data and come up with 3 laws that describe the motions,
although nobody knew why.  Newton decided to apply his gravity formula to
all of that work, and see what happens.

As soon as he started, he knew he was in trouble ... there wasn't enough
Math to do what he needed to do.  So he invented more Math ... the kind
that we call "Calculus" now.  Then he was able to go all the way.  He took
his formula for gravity, and he tested it to see what would a small body do
if it was speeding around a big body, and they were both behaving like his
gravity formula.

When he was finished, he found that WITH his gravity idea, a planet that
traveled around the sun would have to do EXACTLY what Kepler said they
actually do from just watching them.  

That's how Newton knew that his gravity formula was correct, and that he
could go and tell other people about it.

The whole thing happened on account of the two tricks that he used:

#1).  He was born with a good brain.

#2).  He cleared away all the distractions while he was doing his homework.