Plutonium is produced "naturally" in nuclear reactors by bombardment of U-238 with neutrons and the subsequent beta decays of U-239 to Pu-239. If you've got a neutron source (always the tricky part -- the best source is a nuclear reactor), and you've got U-238, you can make plutonium.
Making a bomb with plutonium is tricky, as you've got to assemble it quickly and precisely. Probably just not that hard with today's technology, though. Make sure you have an expert at high explosives on your staff.
You also need a neutron source; the traditional one is a berillyum-polonium device called an "urchin" for some reason.
All of this is 1940s technology. Yes, supercomputers are used to design weapons -- but that's because you want maximum yield for minimum material, or you want a certain type of yield (e.g more radiation and less blast for a neutron bomb). If you just want something that makes a really big bang, that's a different matter. If you can get enough U-235, it's even easier. U-235 is much less toxic than plutonium, and much easier to make go bang.
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