But how do they get pointed from their source in (e.g.) Switzerland to a detector in Italy so precisely?
The idea is to collimate the particles giving rise to neutrinos (pions) with magnets before they decay. In this way, the decay products (the neutrinos) will stay aligned within the beam.
And how can they tell that these particular ones are "your" neutrinos and not from some cosmic event or just from the sun?
There is a probability cosmic neutrinos are within the beam, bu this probability is very tiny. Remember, we need a very well defined energy, a very well-defined direction, etc.. This makes a lot of conditions.