There are a number of ways to measure the rate of photosynthesis; which way is best depends on how accurate you need to be and how much equipment you have available to do the test.
Chlorophyll fluorescence is one method of measurement. Most plant leaves do not absorb 100% of the usable light that falls on them, and must re-emit the unused energy or risk cell damage. Photosynthesis only utilizes a narrow range of wavelengths and re-emits at different wavelengths, chlorophyll fluorescence works by using a sensor to measure the re-emitted light and comparing it to the incident light to calculate photosynthetic efficiency.
Another method is to measure the oxygen gas that is being created by the process of photosynthesis. There are photosynthesis systems that are designed to enclose an entire plant and capture the gases, which are then analysed with an infrared gas analyser. A simpler version of this is often done in school labs by placing an aquatic plant in water in a closed container, exposing it to light, and trapping the gas that is produced. This technique can be used to compare photosynthesis with different wavelengths or intensities of light, or under different temperature conditions.