One simple device is called a cloud chamber. When a particle passes through the vapor, the vapor can condense on the particle which forms a trail of liquid droplets along the path of the particle. You can hook up a camera to take pictures of the tracks. You can also build huge electronic detectors to record the trajectories of new particles produced in a collision. Some of the particles are recorded as having curved trajectories.
Magnetic fields can deflect the path of a moving charged particle.
We can't see the electrons, but we see the remnants of them after they hit the screen and cause it to glow. So far all of the particles mentioned have mass. The photon is the quantum unit of electromagnetic energy, or the basic unit of light. Light, which is just electromagnetic energy, is found in discrete lumps, or quanta, of energy. This is the underlying feature in Modern Quantum Theory.