There are two significant hurdles to building a nuclear weapon: 1) acquiring the necessary quality and quantity of nuclear material and 2) fashioning that material into a workable weapon.
Nuclear bombs are generally made according to one of two designs -- a gun-type assembly or an implosion design.
The gun-type design is the simpler of the two to construct, and works by quickly bringing together two pieces of fissile material, which alone are not sufficient to reach "criticality" -- that is sustain a nuclear chain reaction -- but together form a critical mass.
An implosion device uses an arrangement of high explosives to create a shockwave that compresses the nuclear material. It is more difficult technically to build but requires less fissile material, and can be built from either plutonium or weapons-grade uranium. The gun-type assembly works only with a uranium "pit" or core. The bomb dropped on Hiroshima was a gun-device; Nagasaki's used an implosion design and contained plutonium.
Nuclear material is "fissile" if its nuclei can be split by neutrons in a self-sustaining chain reaction. The splitting or "fission" of each nucleus releases additional neutrons, which go on to split the neighboring nuclei. Each nuclear fission releases a large amount of energy.
In a nuclear reactor this process is controlled and the energy is used to make electricity. In a nuclear bomb the energy is released in an instant producing a devastating explosion.
Uranium is a metal found in the earth's rock and mined much like any other ore. Raw, unenriched uranium is 99.3 percent U-238 and 0.07 percent U-235. These are two of several "isotopes" or forms that uranium can take, and the two most common isotopes found in nature. Uranium has 92 protons in its nucleus. The isotope number, 238, refers to the sum of the number of protons and neutrons, 146, in the atom's nucleus. U-238 is not fissile and will not sustain a chain reaction.
U-235 is fissile. Because of the different number of neutrons in its nucleus (143 versus 146), some properties of U-235 differ significantly from those of U-238. In particular, when an external neutron reacts with or "captures" a U-235 nucleus, the nucleus splits or "fissions." This releases energy.
A chain reaction results when enough neutrons cause the nuclei of neighboring U-235 atoms to split, in turn releasing even more energy. It is this energy or heat, caused by the fissioning U-235 atoms that can be used to generate electricity in a nuclear reactor, or in much larger concentrations, form the core of a nuclear bomb.
The process of separating U-235 from U-238 is known as enrichment. One commonly used method involves spinning a gaseous form of uranium at high speed in a centrifuge. This causes the lighter U-235 to separate from the heavier U-238.
In practice, one centrifuge can only produce a modest amount of separation, so large numbers of centrifuges are employed. A centrifuge cascade gradually increases the concentration of U-235 to various levels of enrichment.