(Disclaimer: my English sucks)
It is a consequence of Lorentz transformation.
Why do we know it is true? Well basicaly Lorentz transformation is coordinates transformation that assumes that speed of light is finite and it is the same in all reference frames.
How do we know that speed of light is the highest possible? If you use Lorentz transformation you will see that both speed and time are transformed using gamma factor. This gamma factor is equal to 1/(1-(v2/c2)), where v is the relative velocity between frames. You can see that if v > c, the gamma factor is imaginary.
If you keep transforming shit using Lorentz tranformation you will sooner or later get to the to the famous formula E=mc2 (yes, it is just another consequence of Lorentz transformation), where m=gamma*m_0 where m_0 is mass of object with v=0.
So if you set v=c, the gamma factor is infinite (1/0) so it means that you need infite energy to get to the speed of light if the mass of the object is not zero.