Shamelessly stolen from PCGamer.
This includes the expansions too, what I had to do was send them photos of the original game keys printed on the manuals.
To get your free key, just head over to the Sega support site and fill in the requisite blanks. It's not unlike the process for getting the free upgrade to the recent remasterings of BioShock, and as with that, you might have to prove that you are in fact a duly entitled owner of the game. "Please note that Sega may need to verify your boxed copies and this may involve them requesting photos of your box or other information,"