Is the source of the sun's energy nuclear fusion or nuclear fission?
The source of the sun's energy is Nuclear Fusion :) Basically, the heat generated within the sun causes the nuclei which would normally repel one another (because they both have a positive charge) to bang into one another and fuse. As a result of the fusion, a new atom is created.
H + H --> He
If you add the atomic numbers of the reactant atoms together you get the atomic number of the product atom. In the above reaction two hydrogen atoms (both with atomic number 1) fuse to form helium (atomic number 2).
Fusion continues until Iron is formed: at which point the star most likely explodes in a supernova. Only at the temperature of a supernova can elements heavier than iron be formed.