Source: Chaisson & McMillan; Chapter 19
The star formation process is amazing. It takes clouds whose properties are; (i) T ~ 10 - 50 Kelvin, (ii) density ~ thousands to millions of particles per cubic centimeter, and (iii) radii, initially around 1 parsec (3.26 light years), and shrinks them to form Main Sequence stars -- objects with central T ~ millions of Kelvin, central densities ~ 1026 particles per cubic centimeter, and radii ~ million or so kilometers (~ 3 light-seconds!).
Once intitiated, the process proceeds roughly as (for a star like the Sun, see Table 19-1 on page 505):
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The preceding discussion concerned the formation of single stars. However, more than half (and perhaps up to 80 %) of all stars are in mulitple (double star, triple star, quadruple star, ... ) star systems and thus an important point to try and understand is how do we form multiple star systems. Furthermore, over the last ten years we have discovered over 182 planets outside of our Solar System ===> Planetary Systems are common. Perhaps many stars which are not in multiple star systems form Planetary Systems ===> It will be even harder to find stars that are solitary travelers in our Galaxy.
The theory of how individual stars form is in fairly good shape. The details of how binary stars form is much less secure.