Make sure your phone is charged and best connected via wifi or if not have a good 3G signal.
From main menu, press menu (bottom left next to the home button)
scroll to bottom and select "about phone"
select "software update"
Then follow the instructions..
Make sure you do not switch off the phone and be patient because it does take a long time, even with a fast internet connection.
I can't help you any further as my phone is now up to date and so cannot replicate the procedure.
Just be patient and wait for it to re-boot itsself a couple of times.
Once it is showing the normal startup screen and stays on it for a while, then try to use the phone and see if it upgraded.
You can check by looking at "Android Version" on the "about phone" screen.
Hope this is of help