To begin with it was believed that light transmitted instantaneously. However now we know that light just moved to fast to be seen.
The first successful measurement was in 1676, by a man named Roemer. He came up with a measurement that light moved a 214,000 km/s. Which was a very approximate evaluation.
Another measurement was obtained in 1728, by a man named James Bradley, he came up with his measurement by observing stellar aberrations. He came up with a value of 301,000 km/s.
In 1849 Fizeau, he used a beam of light and a mirror, he got a value of 315,000 km/s. Foucault improved this measurement a year later, using rotating mirrors he got a more accurate value of 298,000 km/s.