KeepRes=1 will cause Civ3 to keep the resolution of your desktop, whatever that resolution is. It should be after the [Conquests] part of the INI file, such as:
[Conquests]
KeepRes=1
(other things that are already there)
If you are running Vista or later and have UAC enabled, and Civ3 is installed somewhere under C:\Program Files or C:\Program Files (x86), UAC may have prevented your changes; if you re-open the file and it isn't there, it did. In that case, you should be able to work around it by saving the file (while being sure to keep the .ini extension) to somewhere outside of C:\Program Files, and then copying it back in and overwriting the old one, and verifying your changes are present.
If your resolution is greater than 1366x768, but you want it in a 1366x768 window, you'll want to also look up how to do windowed mode. I'm pretty sure it is possible (at least with the CD/Gamersgate versions... less sure about Steam), but I haven't tried that myself so I don't know the process to enable it. Edit: It looks like a patch was released on Thursday to fix the windowed-mode issues I'd read about with the Steam version.