Neutrinos themselves can never be seen. As neutral particles, they do not scintillate or ionise. As particles that feel only the weak force, they barely even interact at all. Despite the fact that you have around 100 trillion neutrinos (mostly from the sun) passing through you every second, the probability of one interacting inside you within your lifetime is about one in four. However, the only way in which neutrinos can be studied is by observing the products of their interactions. If we want to study neutrino oscillations, we need to be able to observe neutrino interactions.
So if the interaction probability is so low, how come we can see any at all in our detectors? The answer: produce a lot of neutrinos and some exceptionally large (or rather, exceptionally massive) detectors. In our experiments, neutrinos are produced in enormous quantities (around [100 thousand trillion] of them!) and observed using detectors with masses of many tens of thousands of tons. Still, in the history of neutrino oscillation experiments, such as T2K, only a few hundred neutrino interactions have been seen at the experiment’s “far detectors”, which are sensitive to oscillations.
But the rarity of neutrino interactions are not our only challenge. Neutrinos interact with the nuclei of the atoms inside our detectors in very complicated ways that are sensitive to subtle details of nuclear structure. For example, the products of neutrino interactions are predicted to look significantly different depending on which model is used to describe the motion of nucleons inside atomic nuclei. It is for this reason that measurements of neutrino interactions are so important. Firstly they allow us to understand the interactions we use to study neutrino oscillations, and secondly they allow a unique study of the nucleus (think about is as seeing what the nucleus looks like when its illuminated by neutrinos).
An example measurement of neutrino interactions in the MicroBooNE experiment (which is a similar type of detector to the ICARUS experiment) shows what can actually be measured. This image of a neutrino interaction shows how an (invisible) neutrino interacts with an argon nucleus, to produce what we detect to likely be a muon, a proton and particle called a pion. The particles are identified by the rate at which they deposit energy within the detector.
