[amalcon]

Basically anyone with access to Wikipedia can design and build a nuclear bomb given raw materials. Not to go into too much detail (both because I'm not really an expert and because it's a dangerous activity even without involving uranium), but the Little Boy bomb dropped on Hiroshima was mechanically very simple. The one dropped on Nagasaki was a bit more complex (still within reach of a skilled machinist), and modern fusion bombs more complex still. Either way, all a relatively weak (but still city-killing) bomb takes is enough uranium-235 and access to a hardware store.

The hard part is getting a sufficient quantity of pure enough uranium-235 (or a few other materials, but that's the easiest one) to support a chain reaction. This is why there's been so little proliferation since the end of the cold war: it's not about the knowledge, it's about resources. Uranium mines and processing facilities aren't exactly subtle.