How do stars survive their own gravitational pull? I read that stars burn hydrogen and helium to fight against gravity. How does burning something help against gravity?
 A: The nuclear fusion reactions do not themselves support the star - what supports the star is a pressure gradient. 
The (spherically symmetric) hydrostatic mechanical equilibrium condition is that
$$\frac{dP}{dr} = -\rho g,$$
where $P$ is the pressure, $\rho$ the density and $g$ the inward gravitational acceleration, at a point that is a distance $r$ from the centre of the star.
In order to generate a pressure gradient, the star needs to be some combination of hotter and denser in its center than it is in its outer parts.
Gravitational compression will heat the star up and temporarily halt a star's collapse, but the problem is that this heat is gradually radiated away from the stellar surface. In order to maintain a high central temperature then some sort of interior energy source is required and that is where nuclear fusion (or "nuclear burning") comes in.
Since these nuclear fusion reactions are highly temperature sensitive, they act as a thermostat in the centre of the star, keeping the temperature just high enough that the nuclear reaction rate balances the radiative losses at the stellar surface. If the star were to contract, the temperature would increase and so would the nuclear reaction rates; this in turn would increase the temperature and pressure in the core even more, the star would expand, thus restoring an equilibrium. 
A: To put it simply, gravitation tends to pull the star together. The things which oppose it are radiation pressure and degeneracy pressures(electron and neutron) generally. In white dwarfs and neutron stars, the latter dominates, while in supergiants, the former dominates. They stabilise the radius of the star, for long periods, which changes later due to the continuos fusion process inside the stars.
