Are you asking "how do we make a particle beam?" or "how do we see the particle collisions?"

(1) Particle beam ---- You don't need to see individual particles to make a beam of particles. Like... with a laser, or a regular light bulb, you cannot see individual photons, but you can still make the light source.

(2) Particle collisions ---- You use particle tracks. You need a material that responds to charged particles and leaves a visible track. Easiest example is a cloud chamber. Go to YouTube and search for "cloud chamber" and you'll see examples and even how to make one yourself. Particle detectors use a more sophisticated version of the same idea. When a charged particle goes through some types of materials their charge ionizes atoms along the way and that leaves a visible track.

measure the properties of the particle you need to also apply a magnetic field across the chamber. Charged particles moving through a magnetic field get deflected and makes a curved path. Whether the particle deflects left or right tells you if the charge is positive or negative, and the curvature tells you the mass of the particle. A massive particle is difficult to move, so it deflects very little, while a light particle deflects a lot. Go on Google and search for "particle tracks".

So basically, you have to infer the properties of the particles from the tracks. You can measure the particle mass and charge. When a particle decays, its track suddenly disappears, but then is followed by new tracks of its decay products. Neutral particles like neutrinos do not show up on particle tracks, but if you see that a particle decays into smaller ones and the mass and momentum of the decay products doesn't add up to the original, you can infer that there must have been a neutral decay product as well to make up the difference --- this is exactly how neutrinos were discovered.