This guy is a good resource: http://www.badastronomy.com/
@aaronb – if you want my opinion, id’ be good to ask for it =) Asking factual questions is probably not a good way to to get opinions. A better question would be “What do you think astronomers do?”
@pjmowbs – eh, sort of. Most people are coming here and asking factual questions, frequently looking for the wikipedia or google answers. Asking for opinions is strongly encouraged, but, you actually need to ask for opinions.
Anyway, there are several kinds of astronomers, the question is largely like asking “what does a lawyer do?” or “what does a physicist do?” —the field is so broad, that it really does range from some guy looking in a telescope to someone looking at raw numbers on a computer having nothing to do with the sky. Heck, the guys who study neutrinos could be considered astronmers, and they’re miles underground! =)