There are two isotopes of Uranium. Natural Uranium consists mostly of isotope U-238, which has 92 protons and 146 neutrons (92+146=238). Mixed with this isotope, one will find a 0.6% accumulation of U-235, which has only 143 neutrons. This isotope, unlike U-238, has atoms that can be split, thus it is termed "fissionable" and useful in making atomic bombs. Being that U-238 is neutron-heavy, it reflects neutrons, rather than absorbing them like its brother isotope, U-235. U-238 serves no function in an atomic reaction, but its properties provide an excellent shield for the U-235 in a constructed bomb as a neutron reflector. This helps prevent an accidental chain reaction between the larger U-235 mass and its 'bullet' counterpart within the bomb. Also note that while U-238 cannot facilitate a chain-reaction, it can be neutron-saturated to produce Plutonium (Pu-239). Plutonium is fissionable and can be used in place of Uranium-235 (albeit, with an entirely different kind of detonator) in an atomic bomb.
Both isotopes of Uranium are naturally radioactive. Their bulky atoms disintegrate over a period of time. Given enough time, (over 100,000 years or so) Uranium will eventually lose so many particles that it will turn into lead. However, this process can be accelerated. This is what the chain reaction does. Instead of disintegrating slowly, the atoms are forcibly split by neutrons forcing their way into the nucleus. A U-235 atom is so unstable that a blow from a single neutron is enough to split it and henceforth bring on a chain reaction. This can happen even when a critical mass is present. When this chain reaction occurs, the Uranium atom splits into two smaller atoms of different elements, such as Barium and Krypton.
When a U-235 atom splits, it gives off energy in the form of heat and Gamma radiation, which is the most powerful form of radioactivity and the most lethal. When this reaction occurs, the split atom will also give off two or three of its 'spare' neutrons, which are not needed to make either Barium or Krypton. These spare neutrons fly out with sufficient force to split other atoms they come in contact with. In theory, it is necessary to split only one U-235 atom, and the neutrons from this will split other atoms, which will split more...so on and so forth. This progression does not take place arithmetically, but geometrically. All of this will happen within a microsecond.
A system of gaseous diffusion is used to begin the separating process between the two isotopes. In this system, Uranium is combined with fluorine to form Uranium Hexafluoride gas. This mixture is then propelled by low- pressure pumps through a series of extremely fine porous barriers. Because the U-235 atoms are lighter and thus propelled faster than the U-238 atoms, they could penetrate the barriers more rapidly. As a result, the U-235's concentration became successively greater as it passed through each barrier. After passing through several thousand barriers, the Uranium Hexafluoride contains a relatively high concentration of U-235 -- 2 to 5% pure Uranium in the case of reactor fuel. If pushed further could theoretically yield up to 95% pure Uranium for use in an atomic bomb. In practice, the total process wouldn't ever be carried out any further than a yield of 90% U-235, and usually less than that.
Afterwards there are further refining processes which include Magnetic separation, and Centrifuge separation. It is really through these processes that the U-235 reaches the high 90% concentration. The Gaseous diffusion is really only taken so far in real life. Gaseous diffusion alone is quite enough for reactor fuel, though.
The minimum amount of U-235 needed to start a chain reaction as described is called SuperCritical Mass. For pure U-235, the value is around 50 Kg (~110 lbs). We never really do get up to pure Uranium, though, so a fair amount more is actually needed. It's dependent on the purity of the material.
Depending on the level of refinement, the warhead design, the altitude of detonation, etc., the destructive force of a Uranium-based device can be anywhere from 1 kiloton to 20 megatons. That measure basically relates to the equivalent amount of TNT -- 1 Kt being 1000 tons of TNT, and 20 Mt being 20,000,000 tons of TNT. Notably, the modern warheads of today don't get any smaller than 20 megatons. It's actually quite valid to have more than SuperCritical Mass as long as you're not higher than SuperCritical prior to detonation. This is one way that larger warheads are created.
Say you have a U-235 detonator... Instead of having a total mass of 50 Kg of pure Uranium, you can have the larger mass pretty close to 50 Kg -- 47 Kg, for instance. The smaller mass plus the larger will be far more than 50 Kg. It is by no means safe to push your luck on that, though.
Note also, that while I say that 20 Mt is the smallest strategic Nuclear Warhead in existence today, that's still VERY BIG. a 20 Mt device can kill people up to 40 miles away from the explosion -- albeit just above 5% fatality rate at that distance. That's why 20 Mt warheads exist only on missiles. You expect a plane to drop a bomb and get 40 miles away before the bomb reaches the airburst altitude of 20,000 ft?
Plutonium chain reactions are generally ten times faster than U-235 reactions, but Plutonium will not start a fast chain reaction by itself. This difficulty is overcome by having a neutron source -- a highly radioactive material that gives off neutrons faster than the Plutonium itself. In certain types of bombs, a mixture of the elements Beryllium and Polonium is used to bring about this reaction. Only a small piece is needed. That mixture is not fissionable itself, but merely acts as a catalyst to the greater reaction.
A Plutonium detonator is far more difficult to manage than a Uranium detonator. The only reason Plutonium is even used despite this difficulty is the cost. Since Pu-239 is created using U-238, it is only slightly more costly -- slightly being a relative measure. U-235 is extremely rare by comparison to U-238, so it is extremely expensive. Secondly, for a U-235 bomb, a far greater amount is needed to achieve SuperCritical mass.
While Uranium can be detonated with a simple 2-part gun-like device, Plutonium needs a 32-part implosion chamber. Pu-239 also needs a higher impact velocity, so the conventional explosives need be much larger. On top of that, the 32-parts have to be blasted simultaneously, so that the Pu sections collide simultaneously. The final difficulty is the adding of the Beryllium-Polonium mixture.
SuperCritical mass for Plutonium is defined as 16 Kg (~35 lbs), although the necessary amount can be reduced to 10 Kg (~22 lbs) by surrounding the Plutonium with a U-238 casing. Notable is the fact that you have 32 pieces to a Pu-239 detonator, so you can go many times higher than SuperCritical Mass-- Another advantage of Plutonium... you can make VERY large warheads with this monster. Take an example where each of the 32 pieces is 5 Kg (11 lbs) -- Each piece is too small to go SuperCritical spontaneously, but at the time of detonation, the total mass is 160 Kg... 16 TIMES what you need for a basic detonation.