Use the dialler and enter this to see your IMEI: *#06# (don't press Call!).
Get your unlock code from the site above.
Double-check you used the correct IMEI number -- it's free to retry!
Turn off your phone.
Open the back.
Remove the battery.
Remove the (Orange?) SIM card.
Insert a SIM card from a different operator.
Replace battery.
Replace back.
Turn on phone.
(If prompted, enter any PIN number that you may have set on the new SIM.)
Now you should be prompted to enter the unlock code. Do it carefully!