See below. During the study period of vaccines, blood work is drawn to determine if an effective immune response develops in the recipient of the study vaccine.
Intense study. Both individual and population studies aid in this conclusion. When you give a vaccine & the recipient develops antibodies, you have step one. When they are exposed to the infection and the antibodies prevent the infection you know it works. It takes decades to find both the vaccine & how high the antibody level needs to be to stop germs, but it is worth it.