The theory behind fusion is actually relatively simple. Fusion has occurred naturally for billions of years from the farthest reaches of the universe to our very own Milky Way. Simply put, fusion is the process that powers the stars.
The energy that comes from the process relies on the joining, or "fusing," of two atoms to form a new molecule. When this larger, relatively unstable molecule splits apart, it releases energy. The most common fusion process occurs with tritium and deuterium as its fuel. Tritium and deuterium are just big names for different isotopes of hydrogen. Need to review some chemistry? Click here to learn more about hydrogen and its isotopes.
So we know that tritium and deuterium fuse and then split apart to create energy. But where does the energy come from? First, lets look at the actual process of fusion. As we all now know, tritium atoms have 1 proton and 2 neutrons, and deuterium atoms have 1 proton and 1 neutron. So when a deuterium and a tritium bang together, or "fuse," a molecule with 2 protons and 3 neutrons is formed. This molecule is inherently unstable, so it splits apart. But it doesnt just revert to a tritium and deuterium. Instead, it splits into an extremely stable helium atom (2 neutrons and 2 protons). The extra neutron is simply released altogether. The animation should provide a better visual explanation.
"But wait", you say, "That still doesnt explain where the energy comes from." There are two explanations for the production of energy, one general and one mathematical. The general explanation is that because the process results in the formation of helium, and because helium is more stable than deuterium and tritium, the system has gone from a state of high potential energy to low potential energy, and thus kinetic energy is given off (click here to review the relationship between potential and kinetic energy).
A more mathematical explanation is derived from Albert Einsteins famous equation, E=mc2. To do the math and see for yourself how the equation relates to fusion, click here. Otherwise, just accept the fact that the total mass of a helium atom and a neutron (the products of the reaction) is less than the total mass of a deuterium atom and a tritium atom (the reactants). The "missing mass" has in fact been converted to energy based on Einsteins equation.