In order to install the firmware, you will have to do it manually by pressing the Option key when pressing the “Check for Update” button in iTunes. Then select the .ipsw file manually. If for some reason your download is a “.zip” file, rename it to “.ipsw” before proceeding.
Warning: This update apparently erases all of the data on your iPhone. Unfortunately this does not work on the iPod Touch.
Related: iPhone 3G: Launch Time and Plans