The discovery of electrons took place when J.J Thompson took the air out of a tube with a fluorescent material in one end. When he gave 10000 V of power to it, he could see some spots in the screen. He called this as cathode rays. Later he named them as electrons.
Goldstein discovered the protons. When he made the pressure inside the container lesser and did the same as Thompson did, he found that a red glow appeared on the end of the tube. He then found that they were because of protons.