When you plug in your phone and iTunes loaded. After that iTunes will check and see is there any new iOS version for your iPhone / iPod and inform you in there is one and ask you to click at the “download and upgrade” button. A lot of people did that by clicking at the “download and upgrade” button.
iTunes will now proceed to download the firmware from Apple’s website but due to network or Apple server congestion issues, people always complain that after waiting the download for hours and it is failed at the end. Some people even gave up upgrading their iOS because of this issue.
I will advice you to manually download the firmware and then ask iTunes to perform the upgrade for you. You can download the firmware from this website: http://www.iphonefirmware.com/firmwares-download/. Of course there are a few more websites hosting iPhone’s firmware but so far I have been using this site and the firmware is clean and original. I assume you know your device’s model such as iPhone 4, 4S, iPod which generation so please make sure you are selecting the right firmware to download.
After the download completed, launch your iTunes and make sure your iDevice is plugged in. If iTunes ask you about the firmware upgrade again, please say no to it. Go to the Summary page, you should see a “Restore” button. Press and hold the shift button and click at the “Restore” button. iTunes will now ask you to locate the firmware file (.ipsw). I assume you know where you downloaded it, so just point iTunes to the file. That’s it, you just wait for the rest of the process to be done by iTunes.
Good luck in upgrading your iOS. 🙂