ELI5: How are nuclear cores, such as the ones used in reactors, created safely?

Having recently watched the Chernobyl mini-series on HBO, one of the questions that keeps coming to my mind is this. If the nuclear material is so deadly that even people in full protective gear are only allowed to be in certain areas of the clean-up for 90 seconds at a time, and some areas were so contaminated that the radiation would destroy any electronics more complicated than a light switch, how do they build the things in the first place? Does the radioactive output become stronger over time?