There are many methods used to measure the speed of light. One is to measure the time light rays require to hit a mirror at a known distance and back. This is how the Fizeau–Foucault apparatus works, which was developed by Hippolyte Fizeau and Léon Foucault.
Fizeau’s setup consists of a beam of light directed at a mirror a number of kilometres away (about 8km). On the way to the mirror from the source, the light ray passes through a spinning cogwheel. At a certain rates of spin, the light ray passes through one gap on the way out and another on the way back, but at slightly higher or lower rates, the beam strikes a tooth and does not pass through the wheel. The speed of light can be calculated by knowing the distance between the wheel and the mirror, the number of teeth on the wheel, and the rate of rotation of the spinning cog wheel.
Foucault had a different setup which replaces the cogwheel with a rotating mirror. Since the mirror keeps spinning while the light travels to the mirror and back, the light is reflected from the spinning mirror at a different angle on its way out than it is on its return. From this difference in angle, given the speed of rotation is known, and the distance to the distant mirror is also known, the speed of light can thus be calculated.
Oscilloscopes with time resolutions of less than one nanosecond are used today to determine the speed of light, as the speed of light can be directly measured by timing the delay of a light pulse from a laser or an LED reflected from a mirror. This method has less precision than other modern techniques, but it can be determined with cheap equipment that can be used in high school.