The Milky Way
Our Galaxy is probably a type Sb or Sc, i.e. it has spiral arms but also a distinct nucleus. Very much like the Southern Pinwheel galaxy M83.

It is about 100,000 light years in diameter (a very large galaxy compared to others) and is thought to contain over 200 billion stars, possibly 400, as well as thousands of clusters and nebulae. All the stars which you can see in the sky at night belong to our Galaxy.
All objects in the Galaxy rotate around the galactic nucleus. Our Sun takes 250 million years to orbit once.
Our Galaxy belongs to a local group which includes several other large galaxies, including Andromeda, and about 30 smaller ones. The nearest galaxy to us is quite small and is about 25,000 light years away.
Our solar system is about 28,000 light years from the galactic centre, inside one of the smaller spiral arms. Most of the rest of the Galaxy, or what we can see of it at least, appears to us as a glowing cloud stretching across the sky. We cannot see most of the Galaxy, however, as it is obscured by interstellar dust.

This NASA image is of Mars passing through the Milky Way. One can clearly see dark clouds of dust obscuring the stars behind.
For more information about the Milky Way look at http://www.seds.org/messier/more/mw.html