Back in Time

How did Newton get the idea of finding this Law whose discovery eventually made him find the other Laws?

The Apple Incident:

One fine evening, Newton happened to be dozing off in a garden under an apple tree when an apple fell on his head, This small event gave birth to one of the greatest discoveries mankind has ever made: Gravitation.After the  apple fell on his head, Newton wondered why it had done so. This was when the notion of gravitation came to his mind.
"Why should the apple constantly fall perpendicularly to the ground? Why should it not go sideways or upwards? but constantly towards the earth's center?", he asked himself.
It is said that Newton spent the whole night trying to uncover the mysterious force which made the apple fall in that particular manner. After a few days he came up with an outstanding theory:
"The Earth draws the apple towards its center, that would mean the sum of the drawing power in the matter of the Earth must be in its center and not in any other side. If matter thus draws matter therefore the apple draws the earth and vice-versa, When the apple falls in the ground, the reason it stays immobile is because the drawing power of the apple and the Earth are compensated."

This is how Issac Newton solved the mystery.
The shocking news is that Newton was the first one to discover gravitation but not the first one to discover the First Law of Motion.

The First Law was actually stated by Galileo Galilei who stated that a force is necessary to change the velocity of an object (acceleration) but not to maintain it. Galileo named the tendency of objects to resist: inertia. Newton's first law is a restatement of Galileo's and Newton honestly gave all the credit to Galileo.

The First Law apparently occurred to many natural philosophers, like Aristotle and Thomas Hobbes. The 17th century philosopher Rene Descartes is said to have perfected the law but was unable to perform any experiment to confirm it.