Who amd how did they measure the speed of light that is known today?
The first accurate estimate of the speed of light was made by the astronomer Romer. It was based on observations of the moons of Jupiter. The first accurate terrestrial measurement was made by Fizeau using a toothed gear, who got within 5% or so of the modern value. Michelson, of the famous Michelson-Morley experiment, began his lengthy and illustrious career in optics by improving on Fizeau’s method. The use of microwave cavities (developed during WWII) improved on optical techniques, and modern electronic techniques gave further improvements (to the point that undergraduate physics majors can measure c to higher precision than did Fizeau). Details are found at the reference.
