To build a device for detecting subatomic particles like electrons, muons, and neutrinos, a cloud chamber is recommended as a viable option. Additionally, large water tanks can be utilized for particle detection, leveraging the interaction of particles with water. Instructions for constructing a cloud chamber typically include using a sealed environment with a supersaturated vapor and a radiation source. Participants in the discussion emphasize the importance of understanding the principles of particle physics and detection methods. Overall, various approaches exist for detecting subatomic particles, with cloud chambers and water tanks being popular choices.