How do nuclear weapons work?

I suggest reading Richard Rhodes books: The Making of the Atomic Bomb and Dark Sun.

Wikipedia also contains good explanations.

There are a number of different types that operate by different principles:

  1. Fission: splitting large unstable atoms into smaller ones with neutron chain reaction.
    1. Gun design, always uses Uranium, fires a bullet and target together with cordite down a cannon barrel to assemble a supercritical mass followed by a pulse of neutrons to start the chain reaction.
    2. Implosion design, can use Plutonium, Uranium, or a composite of both, shaped charge high explosives crush this core to assemble a supercritical mass followed by a pulse of neutrons to start the chain reaction.
  2. Fusion: joining small atoms into larger ones at high temperature and pressure. Note that pure fusion bombs (with no fission component at all have never been built).
  3. Mixed Fission-Fusion: most modern bombs use some mixture of the reactions to optimize the weapon for the mission, the delivery vehicle, and production costs.
  • Fusion boosted low yield tactical fission weapon. These use a small amount of tritium gas inside the fission core to boost efficiency of a tiny low yield core with extra neutrons from the tritium fusion.
  • Multi-stage high yield fusion weapons. These even raise yield by fissioning the normally nonfissionable Uranium-238 isotope with high energy fusion neutrons.
  • etc.