Answered by Zoe Baily of the National Space Centre
The first measurements of the speed of light were made in the 1670s by observing the transits of the moons of Jupiter. It was noticed that the time of the transit was different dependent on the distance between the Earth and Jupiter; taking longer when the Earth was at its furthest.
It was reasoned that this difference was due to the extra time it took for the light from Jupiter to reach us. By making careful observations of the different times of transits at different distances, scientists were able to deduce a speed for light.
Non-astronomical methods can also be used to calculate the speed of light but the great distances between objects in space make it a perfect place to calculate something that travels so fast.