The Sun is a yellow, G2 V main sequence dwarf.  Yellow dwarfs live 
about 10 billion years (from zero-age main sequence to white dwarf 
formation), and our Sun is already about 5 billion years old.

Main sequence stars (like our Sun) are those that fuse hydrogen into
helium, though the exact reactions vary depending on the mass of the
star.  The main sequence phase is by far the most stable and
long-lived portion of a star's lifetime; the remainder of a star's
evolution is almost an afterthought, even though the results of that
evolution are what are most visible in the night sky.  As the Sun
ages, it will increase steadily in luminosity.  In approximately 5
billion years, when the hydrogen in the Sun's core is mostly
exhausted, the core will collapse---and, consequently, its temperature
will rise---until the Sun begins fusion helium into carbon.  Because
the helium fuel source will release more energy than hydrogen, the
Sun's outer layers will swell, as well as leaking away some of its
outer atmosphere to space.  When the conversion to the new fuel source
is complete, the Sun will be slightly decreased in mass, as well as
extending out to the current orbit of Earth or Mars (both of which
will then be somewhat further out due to the Sun's slightly decreased
mass).  Since the Sun's fuel source will not have increased in
proportion to its size, the blackbody power law indicates that the
surface of the Sun will be cooler than it is now, and will become a
cool, deep red.  The Sun will have become a red giant.

A few tens or hundreds of millions of years after the Sun enters its 
red giant phase (or "helium main sequence"; the traditional main 
sequence is occasionally referred to as the hydrogen main sequence to 
contrast the other main sequences that a massive star enters), the Sun 
will begin to exhaust its fuel supply of helium.  As before, when the 
Sun left the (hydrogen) main sequence, the core will contract, which 
will correspondingly lead to an increase in temperature in the core.

For very massive stars, this second core collapse would lead to a 
carbon main sequence, where carbon would fuse into even heavier 
elements, such as oxygen and nitrogen.  However, the Sun is not 
massive enough to support the fusion of carbon; instead of finding 
newer fuel sources, the Sun's core will collapse until degenerate 
electrons---electrons which are in such a compressed state that their 
freedom of movement is quantum mechanically restricted---smashed 
together in the incredible pressures of the gravitational collapse, 
will halt the core's collapse.  Due to the energy radiated away during 
the process process of the formation of this electron-degenerate core, 
the atmosphere of the Sun will be blown away into space, forming what 
astronomers call a planetary nebula (named such because it resembles a 
planetary disk in the telescope, not because it necessarily has 
anything to do with planets).  The resulting dense, degenerate core is 
called a white dwarf, with a mass of something like the Sun compressed 
into a volume about that of the Earth's.

White dwarfs are initially extremely hot.  But since the white dwarf
is supported by degenerate electrons, and has no nuclear fuel to speak
of to create more heat, they have no alternative but to cool.  Once
the white dwarf has cooled sufficiently---a process which will take
many billions of years---it is called an exhausted white dwarf, or a
black dwarf.