The first thing that astronomers noticed is that the Galaxy is very dusty, making it hard to see through in certain directions. We're in the position of being in the middle of the forest, trying to determine its shape and extant, but all the trees keep getting in the way. Nevertheless, by combining the results from several different techniques (radio astronomy vs. visible vs. infrared light, for example), and by drawing analogies with more distant galaxies that we can see in their entirety, we've built up a picture of our home galaxy that most scientists are confident of.
Our galaxy is big- 20,000 parsecs (60,000 light-years) in diameter, to a first approximation. Not the largest of galaxies, to be sure, but hefty. The exact count of its stars in a matter of debate, but everyone agrees that the number lies between 100 billion and 500 billion.
The Galaxy's shape is round and mostly flat- sort of like a cross between a CD and a fried egg. The Thin Disk- the midplane, where we live- contains the famous spiral arms. It is only a couple of thousand parsecs deep but 20,000 parsecs across. In the center of the Galaxy, like the yolk of the fried egg, is the bulge of the central Core.
It was once thought that one place in the Galaxy was as good as another as far as the chances for finding a habitable planet were concerned. More recent thought on the subject is that this is not strictly true- there is probably a zone of maximum probability, a gigantic annulus, where the conditions are right for the long-term development (important emphasis) of Earthlike planets. This is known as the Galactic Habitable Zone, or GHZ for sort, and it is analogous to the ecosphere that rings a Sunlike star. While its exact boundaries (like those of a stellar ecosphere) are a matter of debate, the concept itself is not.
