My Grandfather had a similar need, he hand wrote his memoirs on paper and then wanted to turn them into a self published book.
The best way to do this is to get someone who has good English skills and is fast at typing to do it.
Speech recognition software is not use-friendly for those who are not tech savvy, I wouldn't suggest it is an easy way for him to use a computer. They are also incredibly inaccurate.
I would argue at this point Google Voice and Apple's Dictation features have better recognition than the leading product on the market as they learn from their users over time where as most standalone products have limited data to work from.
However it's worth a try, for OS X you'll need Nuance's Dragon Dictate for Mac it works I've tried two versions but it's not great however. It is pretty pricey, and you'll need to get the headset, it won't work very well with a poor quality microphone or just a ambient mic on your Mac.
They also have an app on iTunes that is free, again it works okay, but not great.
The main issue with dictation is that you have to say all the punctuation and often words are misheard and that can in turn confuse it with the next few words, it's also very difficult to think of what you want to say in written language quickly enough.
In conclusion, I honestly wouldn't recommend voice recognition, especially if you are hoping to make it easier for him. I would suggest he uses an iPad and types it, or you sit with him and he dictates it. My Granddad had my Mum do this in the end, 3-4 months of weekly meet-ups he was very happy and they had a great excuse to spend time together.
Best Answer
If your iOS device is on version 5.0 or higher, then yes, you can do it directly from the handset by going to Settings/General/Software Update.
If you're on iOS 4.x then no, you will need a computer to do this.
To upgrade in your situation, I would recommend the following steps: 1) On your new laptop, open iTunes, and in the preferences on the devices tab, make sure Prevent iPods, iPhones, and iPads from syncing automatically 2) Plug your iPhone in to the new laptop, and in iTunes, select the iPhone on the left pane. 3) Click Check for update.
It should find a newer version, and start to download the file. You can now disconnect your iPhone from your new laptop.
Once it has downloaded this file, you should be able to find it on an OSX system in your home folder/library/iTunes/iPhone Software Updates. On Windows it should be in your user profile folder\Application Data\Apple Computer\iTunes\iPhone Software Updates.
You can copy this file to your old computer, and then plug your iPhone in to that.
On a Mac, hold the Option key (alt on modern keyboards) (shift on Windows) and click Check for update. You should now be able to manually navigate to the ipsw file you just copied over.
It should now start the update process on your iPhone.