Why do stars undergo nuclear fusion? This might sound silly. But we always talk about nuclear fusion in stars and I have always wondered why this process happens at all.
Is it inevitable for fusion to happen at the temperature and pressure present in a star? 
 A: Think of 2 hydrogen atoms or, protons more accurately since at those temperature the atoms don't have electrons, it's more of a soup.   So, 2 protons, both positively charged so they repel each other, crash into each other pretty rarely, cause it's still a lot of empty space, but they do make contact every so often.   The energy required to get 2 protons or any other atomic nuclei to touch is very high.  This is called the Coulomb barrier
That's basically all fusion is, it's when 2 atomic nuclei, which naturally repel each other, get pushed close enough to touch and fuse into 1 nuclei.
Once they touch, in the case of protons, then it's a matter of what quantum combination is most likely to follow.    Protons actually don't like each other so much more often than not, they'll just say "lets not do this" to each other and they effectively bounce off each other, basically staying hydrogen.
About one time in a million . . . or so, the protons will stay and fuse but for this to happen, one of them has to become a neutron, because 2 protons aren't a stable nucleus.   So in this rare occurrence when they do fuse, one proton kicks out a positron, a neutrino and a gamma ray, essentially getting the energy to do this from the fusion and you're left with a proton-neutron bound together (Deuterium) from a proton-proton collision.   This happens rarely but because the sun is so large and there's trillions and trillions of proton-proton collisions every second, you get trillions and trillions of Deuterium nuclei formed every second and Deuterium, unlike protons, is very eager to merge with a proton or another Deuterium so, from there, the process continues.
This is also why hydrogen bombs are made with Deuterium, not hydrogen - hydrogen is much much harder to create fusion with.
Because of this, the sun effectively burns very very slowly, but all that's needed is sufficient temperature and pressure to break the coulomb barrier.
A: Its just a consequence of what concentrates the fuel/contents of a star together in the first place, I think? Stars usually form by the collapse of gas clouds onto themselves. These collapses generate high temperature and density and are ideal places for nuclei to 'bump' into each other and also, the high amount of energy nuclei can possess in such a situation is an added bonus. These are ideal conditions for fusion. Once fusion starts, the energy supplied by it self sustains the process, along with the intense pressure generated by the inward gravity of the star.
A: The Coulomb barrier for protons is on the order of $10^6$ eV. Treating the Sun's core as a gas at 15.7 million kelvins, the mean kinetic energy of the protons is $2\times10^3$ eV. A quick partition function estimate of the probability of protons having enough kinetic energy to overcome the Coulomb barrier yields a probability of $10^{-257}$. Considering the entire Sun has an upper limit of $10^{56}$ protons,  and there are on the order of $4 \times 10^{38}$ protons per second converted in the proton-proton cycle, it seems there must be another process involved beyond temperature and gravitational pressure.
Quantum mechanical tunneling of the Coulomb barrier is a third phenomenon necessary for fusion to occur. The high temperature and high proton density are both necessary to boost proton energy so that the remaining energy height and thickness of the barrier are reduced so that tunnelling even has a reasonable probability (>$10^{-20}$).
A: To make fusion occur, large amount of activation energy is required. Once running, it will keep going. 
The reason why the surface of a star of a large mass is a suitable place for fusion to occur is its large gravitational force on small atoms like hydrogen. This strong gravitational force makes for a strong pressure on the gas, and according to the ideal gas law:
$$\frac{PV}{nT} = R (R = Gas Constant) $$
increasing pressure will increase temperature proportionally. If the temp. is high enough, the gas particles will this be able to ram into each other with enough kinetic energy to activate the fusion reaction.
