The hard part is getting the material — enriched uranium or plutonium :-)
Other than that it's trivial to make gun-type device similar to the Hiroshima one, but it requires much more material as you need a critical mass to sustain a chain reaction.
A more advanced implosion version crushes the material and so increases its density, so you need less material. The usual method is to make the material into a sphere and symmetrically detonate chemical explosives around it. The hard part is ensuring these charges denotate symetrically, as even several microseconds' delay between their detonations prevents the material reaching critical density.
About "getting the material", you could enrich uranium by reacting it with fluorine to make uranium hexafluoride, and spin it in a powerful centrifuge. Ordinary uranium contains mostly heavier U-238 (not useful in your case) and lighter (useful) U-235. The centrifuge very slowly separates the useful isotope from the less useful "depleted" uranium.
As for politically hard part, try building such a centrifuge and you'll soon have the IEAE (or worse) knocking on your door!