Civ3 doesn't support a windowed mode. The article linked will work, but may not be an option for everyone.
What you can do is mod your .ini file to have the lines KeepRes=1 and Video Mode=1024 in there. This will keep your desktop resolution the same, and force Civ3 into a 1024x768 'window' in the upper left corner of the screen. This is not a true windowed mode, as you can not move it around or resize it.
You can always Alt-Tab out of Civ3, or hit the windows key and have access to the task bar from there.
