Star Formation:
Stars form from clouds of gas and dust (100 times as much gas - mostly hydrogen) in the interstellar medium (example). Some clouds are dense enough to become dark with dust and form molelcules. Within them, cores become yet denser until they can begin to collapse under their own weight, overcoming the turbulent motions and magnetic fields which were holding them up. They start with a little spin, which becomes faster and faster as they contract from a scale of a few light years across to a few hundred AU across (example). Given the typical amount of spin, this smaller scale (like our solar system) is the point at which centrifugal force will balance gravity. The cloud collapses to its equatorial plane (examples), forming a disk. Angular momentum must then be transferred through the disk (spiral arms are one way) in order to allow material to spiral down to the star. Near the star more angular momentum is shed through a process involving magnetic fields, which gives rise to spectacular jets (examples) of material leaving in the poleward directions. These jets may extend back out for a light year or more, and add new turbulence to the cloud. The disk is obviously a site where planetary formation might take place. When a high mass star forms, it is both very luminous and produces a strong wind of material flowing away from it (example1, example2). This can seriously disturb low mass star formation for light years around it (and may also promote stars forming through compression of the cloud). Before low mass stars have even had a chance to reach the main sequence, the high mass star will explode violently, further disturbing the environment around it and seeding it with new heavy elements.

Stellar Evolution: Low Mass Stars:
If a star is too low in mass (less than 7.5% the mass of the Sun), it will not really be a star at all. Such objects never have a main sequence phase; they are brightest and hottest when they form (M spectral class), and then forever cool and get dimmer. They are called brown dwarfs. Below 6% the mass of the Sun, they do not even get hot enough to destroy lithium - this has provided one way of distinguishing them from low mass stars (which all destroy lithium) and dozens are known. Finally the brown dwarf will cool below the minimum main sequence temperature (about 2000K) and then its state is more obvious. We know one such object : Gl229B at about 1000K. Contrary to what your book says, brown dwarfs may be as common as stars - its just that they are very hard to see.

The evolution of stars up to about ten times the mass of the Sun is similar. After forming and reaching the main sequence, they remain there for a much longer time. During this phase they are burning  hydrogen and increasing in brightness only a little. When the core is converted to helium, it can no longer produce energy and begins to collapse again. This raises its temperature and density, as well as that of the surrounding regions. Around the core, hydrogen can fuse again in a shell. This shell burning causes the outer parts of the star to swell, so the surface becomes bigger and cooler (the subgiant phase).
The core becomes degenerate (electrons are forced into high energy states by a quantum mechanical principle); its pressure then is not thermal and does not respond easily to heat input. Shell burning continues to brighten the star and swell it (the red giant phase). When helium ignites, the increased heat does not expand the core but does make the helium burn faster. This runs away with itself in the "helium flash", until the core is so hot that the degeneracy is lifted. We do not see this flash as it is buried down inside the star. The star ends up responding by lowering its luminosity in non-degenerate helium burning and shrinking a little, leaving the tip of the red giant branch.
This "helium main sequence" can take the star over to the yellower "RR Lyrae" phase (where it pulsates) depending on its composition (a low fraction of heavy metals), or leave it near the red giant branch (for compositions like the Sun). As the helium core burns to carbon (triple-alpha chain) and begins shrinking again, the star brightens and swells  and the envelope of unburned hydrogen becomes increasingly less stably bound to the star. It finally cools enough to form dust, and the intense light from the core coupled with the dropping escape velocity (because the radius is getting so large)  causes the envelope to be ejected.
This phase produces what is call a "planetary nebula"; the expanding envelope leaving the star. The UV radiation from the hot core ionizes it and makes beautiful objects in the sky up to several light years in extent. Some products of the nuclear burning (C,N,O) and dust are injected into the interstellar medium, to await a new star formation phase. The core, unable to generate further energy, shrinks to the size of the Earth and becomes a "white dwarf".

Stellar Evolution: High Mass Stars:
This begin as above, except that the timescales are very much shortened. They differ at the helium burning phase, since the weight of the overlying star allows helium burning to occur before the core is degenerate. It also allows the burning to continue with carbon, and all the elements up to iron can be produced by nuclear fusion in the core. There will be formation of a succesive layer of shells, each going through the next heaviest cycle, as the core shrinks down. Because each heavier fusion cycle is less efficient, the time spent on each gets shorter. The cycle leading to iron is only a few minutes long. No energy can be extracted from iron fusion (it costs energy), so the star is out of luck then. The core collapses, and the pressures are to great to even stop at the white dwarf phase. A supernova explosion immediately occurs, blowing off all the outer processed layers and leaving a neutron star or black hole in the center.

Stellar Lifetimes:
It is fairly easy to estimate the main sequence lifetime of a star. It is easiest to do everything relative to the Sun. For the Sun, you can estimate its lifetime using the current measured solar luminosity, the amount of hydrogen which must be used up per second to produce that luminosity, and the fact that the Sun can only make use of about 10% of its hydrogen for fusion (since the inner part of the Sun does not mix by convection and so does not drag down hydrogen from higher up). This gives a lifetime for the Sun of about 10 billion years. Other stars lifetimes will be proportional to that by the ratio of their mass over their luminosity (p. 395 in the text) as measured in solar units. Thus, a star which has ten times the mass of the Sun, but ten thousand times its luminosity, will have a lifetime a thousand times shorter (or 10 million years). Massive stars live short lives because they are fabulously profligate with their (greater) resources. Similarly, stars less massive than the Sun can live much longer than it because they are so faint.