Here's how:

Make sure your Windows video display is in 16-bit mode (Control Panel...Display properties).
Right-click the shortcut icon you use to launch the game and select Properties from the pop-up window (if you launch the game from the start menu, you'll have to locate the shortcut via Windows Explorer).
On the properties screen, select the Shortcut tab.
In the target field, add the following line at the end of the shortcut (after the ending quote):
-w -r640x480
where the "640x480" can be whatever your desired screen resolution is.
For example, to run the game in an 800x600 window, your target might look something like this:
"H:\Program Files\Maxis\SimCity 3000\Game\SC3.EXE" -w -r800x600

Valid resolutions include, but may not be limited to: 640x480, 800x600, 1024x768, 1280x1024.

Notes: if Windows isn't running in 16-bit color, the game will switch to full screen regardless of what you add to the target. In addition, on Windows NT (and possibly 95 and 98), SimCity 3000 will soak up all your CPU cycles even if it is minimized.

Tip: if you want an option to run the game in a window, copy your shortcut so that you have two of them. Only modify one shortcut and rename it to "SimCity 3000 Windowed" or something.