If you want to update your phone's iOS version (the page that you posted from is for iTunes on a computer) then you can either do it directly on your phone via Settings > General > Software Update option (if your tagline isn't correct and you aren't already on iOS 5+ then the option won't appear), or you can update via your computer's iTunes.
To update via a computer, connect the phone to your computer's iTunes and copy any purchases off it to your computer via File > Transfer Purchases (File > Devices > Transfer Purchases on iTunes 11). You may also want to copy photos and any important documents off the phone as well e.g. via the file sharing section at the bottom of the device's apps tab when connected to iTunes, via wifi, email, dropbox etc - they should be included in the backup, but it's best to have a copy of them outside of the backup just in case. You can then force a backup of the phone by right-clicking the phone 'Device' on the left-hand side of iTunes and selecting 'Backup'.
Then start the update by selecting the phone on the left-hand side of iTunes (on iTunes 11 you can enable the left-hand sidebar via option-command-S on a Mac, control-S on a PC), and on the Summary tab on the right-hand side clicking the Check For Updates button