They don't take pictures, the particles are recorded by a variety of detectors. For example, a wire chamber records particles through the ionization they cause in a very diluted gas, those ions are then accelerated by the electric field in the chamber and causes a blip when they hit one of the wires. As the particles are tracked all the way through the detector, they can know the state both before and after the collision.

Then there are calorimeters that absorbs the debris from the collision and measures the energy of it.