You need to modify your .ini. Depends on what version you're playing, but the .ini will be in the same directory as the executable.
Add the following lines to your .ini to make it 1280x1024:
KeepRes=1
There is no true windowed mode, but you can fake it. It's not very good tho. Add the following lines to your .ini to make a 'windowed' mode:
Video Mode=1024
KeepRes=1. This will force Civ3 into the upper left hand corner of the screen, leaving you the bottom section and some of the right side of the screen. However, you can't move it. Do note the space in 'Video Mode'.