Where to begin tends to be the most difficult decision when describing any system, and stars are certainly that. Since this will be a bit of a "flying by the seat of our pants" discussion of stars, I'd like to begin with some direction, at least a bit of an idea where we're headed to justify the bit of seemingly disparate and irrelevant topics that are necessary background. I will assume you've watched enough Nova programs to have a basic understanding of space and how it works so I'll quickly gloss over the bare basics and present them in a manner my differential equations professor jokingly put it regarding quantum physics, "We have to approach this like a religion. I'm not telling you why, but you have to just trust me that this is true, and that you could make a bomb and it would blow up."
Buzzing through the basics
We live on a planet called Earth. It is mostly rock and orbits an otherwise insignificant and regular star we call the Sun. We have a single satellite orbiting us, the Moon. We rotate around and face the Sun about every 24 hours and go around the Sun once about every 365 spins, or days as we like to call them. There are many other bodies orbiting the Sun: 8 planets, numerous dwarf planets, belts of millions of smaller objects, irregular comets, and eventually a massive cloud of objects extending to 200,000 times the distance of the Earth, about 3 light years out and still orbiting our Sun. Our system is again, relatively unremarkable (except it's our neighborhood, of course) and sits in one arm, well out from the center of a relatively unremarkable galaxy, in a relatively unremarkable cluster of galaxies... you get the point. Space is big, we're not.
Thanks to Einstein, we have established that there is a speed limit in all of this: c, the speed of light, approximately 300,000,000 meters per second, or for you Americans, 186,000 miles per freakin' second. If you shine a laser at the moon, it'd take 1.4 seconds to see the dot, that's it. Now, remember that Oort Cloud I mentioned, extending from about 1900 AU (1 Astronomical Unit = the distance from the Earth to the Sun) to 200,000 AU? It takes light about 3 years to get from the Sun past the cloud by some estimates.
...are really, really, really far away. We can't go to any (yet), we can't bounce RADAR off them, we can't throw sticks at them, and we can't judge their maturity by insulting their mother. So how can we know much about them? Light. The only things we know about the universe outside our own solar system we know by catching light and analyzing it and thinking reeeal hard (something we humans pretend we're good at).
Light doesn't seem like it'd shed much--well, light--on stars. But luckily it comes in many flavors and can be captured and measured. Light propagates like a wave and interacts with matter like a particle. Obviously, since we are matter and all of our instruments are matter, we care deeply about collecting and measuring these massless particles, photons. Each one carries with it a bit of energy based on its wavelength (I know, a particle with a wavelength? It's a model, go with it.) While this doesn't sound like much, as we will see, it's more than enough information to build incredible models. I will devote an entire post to light at a later date as it lends itself useful to other discussions, but in brief, light is just what we call electromagnetic waves. What you and I see as different colors are just photons with different wavelengths in a range we can pick up with our eyes. For a good consideration, "Blue" is the name we give light at around 475 nm (nanometers), and "Red" is what we call 700 nm. By the same token, we could call "X-Ray" a color, "Microwave" a color, and "Radio" a color--just colors we can't see with our eyes. They're still light!
NOW! What the hell does that all mean? Think of a telescope as a precise photon catching bucket. If we point our telescope right at a star and catch some of the photons it shot at us years ago that are just now arriving, we can tell an unbelievable amount of information just by dissecting our catch! First, the obvious, how many photons did we catch? Brighter stars send out more photons per second and so more of them land in our bucket, BUT, a brighter looking star might just be much closer than a dim star, so we catch more of its photons! More on that in another post, look for parallax (essentially looking at the same star from two different places--say, the Earth on June 25 and December 25--and using depth perception, like our two eyes!) We also know very precisely what sorts of wavelengths are captured too, betraying very accurately the various atoms responsible for either emitting those photons or absorbing those that we would expect to catch but don't.
This has been a massive first post, but it is meant to be a bit of an overarching summary of how we can know what we know and will be very useful in providing "bins" of concepts, which we will soon fill with real materials and justifications! I will be creating graphics for these posts as time permits (largely for my own enjoyment) and encourage you to check back soon. This first post has spent too long looming in the distance and now that it's done, we can proceed at a more reasonable pace to fill in the gaps and do some real learning!