Fusion!

Main sequence stars produce most of their energy by hydrogen fusion (also called hydrogen burning). The net reaction here is that four protons (hydrogen nuclei) and a couple of electrons fuse into a single helium nucleus - two protons and two neutrons - along with a heck of a lot of outgoing radiation and neutrinos. But this same net reaction can happen along two very different pathways: the proton-proton chain (PPC) and the carbon-nitrogen-oxygen cycle (CNO cycle). The proton-proton chain reaction works basically as you would expect:
1. Two protons fuse into a deuteron (deuterium nucleus - a proton and a neutron), a positron, and an electron neutrino
2. A deuteron and a proton fuse into a He-3 nucleus and an outgoing photon
3. Two He-3 nuclei fuse into a He-4 nucleus (just an alpha particle) and two protons

The net reaction here is just four protons -> one alpha particle, and it has an efficiency of around 0.7%. Not too high, but when you consider how much hydrogen there is in a star, you start to understand how they can radiate so much. In order for the PPC to work, the temperature of the star's core (where fusion is actually taking place) needs to be above around 2*10^6 K.

The CNO cycle has the same net reaction as the PPC, but it is catalyzed by carbon-12. It's a 6-step process in which carbon fuses with a proton to create a nitrogen, which decays into a heavier carbon. The heavier carbon then fuses with another proton to produce stable nitrogen-14 and some radiation. The nitrogen fuses with a third proton to produce an unstable isotope of oxygen, which then decays into nitrogen-15. Finally, the heavy nitrogen fuses with a fourth proton to produce a carbon-12 atom and an alpha particle. The net reaction here is the same, so the net efficiency (energy produced out of the total mass energy of the constituent parts) is the same as for PPC. But CNO has a much stronger dependence on the temperature of the star (T^19.9 as compared with T^4 for PPC) and doesn't kick in until temperatures around 10^7 K.

It turns out that the sun mainly burns hydrogen by PPC, as its core temperature is not quite high enough for the CNO cycle.