Reprocessing is the chemical operation which separates useful fuel for recycling from nuclear waste.
Used fuel rods have their metallic outer casing stripped away before being dissolved in hot nitric acid. This produces uranium (96%), which is reused in reactors, highly radioactive waste (3%) and plutonium (1%).
All nuclear reactors produce plutonium, but military types produce it more efficiently than others.
A reprocessing plant and a reactor to produce sufficient plutonium could be housed inconspicously in an ordinary-looking building.
This makes extracting plutonium by reprocessing an attractive option to any country wishing to pursue a clandestine weapons programme.