Though the new firmware can easily be downloaded when you connect your device to iTunes, but if you’re facing any connection trouble using it, then you can always do the procedure manually. Here’s how.

Download the ipsw file (Its the firmware) from the link given below:

Download iPhone OS 3.1.2 for iPhone 2G
Download iPhone OS 3.1.2 for iPhone 3G
Download iPhone OS 3.1.2 for iPhone 3GS

Go in the recovery mode, go to iTunes, select your device, click on Restore while pressing the Shift key, it will open up a window asking for the location of ipsw file, select the file and you’re done.

Using this method, you can manually install Firmware 3.1.2 on your iPhone/iPod touch without using iTunes.