A Gravitational Journey

One of curses or blessings of being a nerd is that just out of the blue a crazy question pop into your head and you cannot rest until you settle it. A few weeks ago suddenly, and I swear to the principles of science, with no trigger whatsoever, this question came to my mind, how stars are formed, i.e., if we have a huge cloud of gas in the vacuum of space, how it get dense enough to form a star? And another question that immediately followed was how the gravitational pull of the material inside a star causes a star to collapse into a blackhole? Is it possible to answer these questions with the physics I know?

To simplify this problem assume that we have a homogeneous sphere and we want to calculate the exact pull of gravity in every particle of gas inside this sphere from the material in the rest of the sphere.