I bought this game under the assumption it worked on Windows 7. I start up a Free Play game and right before the actual game kicks in, the screen turns black and then it crashes.
What should I do?

...now I see that forums poster helen.burt had the same problem, and the solution was simply changing screen resolution in the game options.
http://www.gog.com/en/forum/the_settlers/crashing_when_attempting_to_start_a_new_game
hooray!