When we think of stars we usually imagine our Sun. But the simple fact is that the Universe is made up of many different types of stars. In fact looking into the heavens most stars look very different, and some aren't really stars at all. So here is a run down of the most common types of stars in the galaxy.
A star is said to be born once nuclear fusion commences in its core. At this point it is, regardless of mass, considered a main sequence star. This is where the majority of a star's life is lived. Our Sun has been on the main sequence for about 5 billion years, and will persist for another 5 billion years or so before it transitions to become a Red Giant Star.
Once a star has used up all of its hydrogen fuel in its core it transitions off the main sequence and becomes a red giant. Depending on the mass of the star it can oscillate between various states before ultimately becoming either a white dwarf, neutron star or black hole. One of our nearest neighbors (galactically speaking), Betlegeuse is currently in its red giant phase and is expected to go supernova at any time.
3. White Dwarfs
When low-mass stars, like our Sun, reach the end of their lives they enter the red giant phase. But the outward radiation pressure overwhelms the gravitational pressure and the star expands farther and farther out into space. Eventually, the outer envelope of the star begins to merge with interstellar space and all that is left behind is the remnant of the star's core. This core is a smoldering ball of carbon and other various elements that glows as it cools. While often referred to as a star, a white dwarf is not technically a star as it does not undergo nuclear fusion. Rather it is a stellar remnant, like a black hole or neutron star. Eventually it is this type of object that will be the sole remains of our Sun billions of years from now.
A neutron star, like a white dwarf or black hole, is actually not a star but a stellar remnant. When a massive star reaches the end of its life it undergoes a supernova explosion, leaving behind its incredibly dense core. A soup-can full of neutron star material would have about the same mass as our Moon. There only objects known to exist in the Universe that have greater density are black holes.
5. Black Holes
Black holes are the result of very massive stars collapsing in on themselves due to the massive gravity they create. When the star reaches the end of its main sequence life cycle, the ensuing supernova drives the outer part of the star outward, leaving only the core behind. The core will have become so dense that not even light can escape its grasp. These objects are so exotic that the laws of physics break down.
6. Brown Dwarfs
Brown Dwarfs are not actually stars, but rather "failed" stars. They form in the same manner as normal stars, however they never quite accumulate enough mass to ignite nuclear fusion in their cores. Therefore they are noticeably smaller than main sequence stars. In fact those that have been detected are more similar to the planet Jupiter in size, though much more massive (and hence much denser).
Most stars we see in the night sky maintain a constant brightness (the twinkling we sometimes see is actually an atmospheric effect and not a variation of the star), but some stars actually do vary. While some stars owe their variation to their rotation (like rotating neutron stars, called pulsars) most variable stars change brightness because of their continual expansion and contraction. The period of pulsation observed is directly proportional to its intrinsic brightness. For this reason, variable stars are used to measure distances since their period and apparent brightness (how bright they appear to us on Earth) can be sued to calculate how far away they are from us.