Einstein developed special relativity as a strong logical and mathematical structure based on two fundamental postulates. The consequences deduced from them are special relativity theory, which is the subject of this site. If the postulates are correct, then so is special relativity. Conversely, the experimental evidence that special relativity is correct confirms the postulates.
Postulate 1: The constancy of the speed of light.
The speed of light in a vacuum is always measured to be the same value by any observer. In particular it does not depend on the motion of the observer or the light source.
Postulate 2: The principle of relativity.
It is remarkable that a theory as deep and strange as special relativity follows from these quite simple postulates.
Actually, a range of subtler and more technical postulates are required involving the sameness of space in different directions and at different places, and such like. However, these are simply parts of our everyday understanding of space and time that remain true in special relativity.
You can read the original statement of the postulates by Einstein in the introduction to his 1905 special relativity paper.