The bulk of the work is done in a free application called MediaCoder. Go to the site and download the latest version. Once this is done, start the application and you will see its interface, with all of its menus and buttons.
Once the app is started, you can access a special menu item to configure all of the settings for the iPhone and iPod Touch. This setting is found under the Features | UI Plugins | Digital Media Players | iPhone / iPod. Choosing this menu option will open a new dialog with device-specific controls and also reconfigures other elements of the interface for the iPod.
Unfortunately, while it sets most things right, one setting that usually does not get selected correctly is the resolution / aspect ratio of the output video. While the default one selected does fill up the entire screen on the iPod Touch / iPhone, it distorts the image of all videos that are made in a 16 X 9 aspect ratio. The way to fix it is to choose the 480 X 272 resolution from the list.
Once everything is configured, simply add the videos that you want to convert using the Add icon on the toolbar and launch the conversion with the Start button on the far right side of the toolbar. The result will be a .MP4 file that can then be inserted in iTunes to sync to your device. Enjoy!