It's just a standard-sized screwdriver. It's a long, large-ish one - not a jewellers one or anything - but it does have quite a pointed tip. Plenty of different screwdrivers will work, though, just make sure they're pointy.

If your key-post (the white bit) is actually sticking out the front and there's nothing in it, then it's even easier - just put the spring around the white bit and push the key into the hole in the keypost.
Make sure your key has its own little plastic post as well to insert into the post sticking out of the keyboard itself.
edit: Looking at the old photos again, you're probably OK and not needing to remove the back after all - but then I don't understand why you're having a problem. Are you sure there's nothing left of the old key stuck in the post?