How was Newton's first law discovered?
This is the way I remember it...
Galileo Galilei already noticed that if you have an object, say a wooden block, on a surface and you kick it then it will move and after a while it will stop.
But, if you smooth out the surface the object will stop after a longer distance!
So Galileo imagined that making the surface "infinitely" smooth the object would never stop.
Newton realized that this smoothing process was needed to eliminate an entity (a Force) that was causing the object to stop and deduced that if there were no Forces acting, the object would continue to move!
So, basically, after the first kick (the Force that causes the start of the movement from zero to a certain speed) ends, so that no force is "pushing" and the object moves (with a constant speed), the object would move forever unless the surface would exert a counter Force to stop it.