How did Einstein conclude that light travels at the same speed for all observers?

[mjolnir80]

how exactly did Einstein come to the conclusion that light travels at the same speed regardless of the observers own speed?

 

[mgb_phys]

It's not really a concusion it'sthe starting point.
There is a much earlier principle of relativity that says the laws of physics are the same for any moving body - so your physics test doesn't give different answers in the summer and winter when we are moving in opposite directions around the sun.
But Maxwell's laws give a fixed speed for light.
This would destroy the earier principle, because we could use a measurement of light speed to say how we were moving.

Einstein said 'what would we have to do to make the first principle work?' = the speed of light would have to be the same for everyone.
From this postulate (=claim) all the effects of special relativity follow.

 

[HallsofIvy]

Also a number of experiments, in particular the Michaelson-Morely experiment, showed that light could NOT be used to determine an "absolute" speed.