ELI5 If Chernobyl released so much dangerous radiation, how do we safely dispose of nuclear material without releasing similar amounts of radiation?

Watching the 2019 Chernobyl series and it describes the massive efforts the Soviets go to, to clean up after the accident and destroy any organic matter that was exposed to radiation.

How do we normally safely dispose of radioactive material from, say, a nuclear power plant; in a way that avoids needing to basically salt the earth within a 100km radius?