What will sell Superman as existing in the real world will peoples' reaction to him. Look at the movie Independence Day-- conceptually, the idea that flying saucers would appear above every major city is somewhat absurd, but the way the regular people from all walks of life react to it is what sells it. The existence of a comic book-style superhero in reality should raise all manner of questions. The military, police, politicians, average Joes and Jodies living out their lives... All of them should have believable reactions to this colorful new character who has appeared in their city.
Me and my brother actually had a few ideas for a real-world Superman story that we thought were pretty good. One of them was that the police, fire fighters, and other emergency workers were all afraid of Superman because he's threatening their job security, but then later Superman would give some kind of speech about how he's there to do the things that normal people can't do on their own, and how things like putting out fires and catching robbers are not a job for superman. This would actually be a reference to the Fleischer cartoons, because if you notice the Fleischer Clark Kent would not say "this looks like a job for Superman" until it was obvious that the police were overwhelmed and needed his help. This would also explain why Superman hasn't turned Metropolis into a crimeless utopia, because he does not want to overreach.
Another idea, which chronologically would occur before this, was that some people would start to get the idea that Superman is such a goodie goodie that they can get him to do whatever they want, to the point where a crazed Superman "fanboy" of sorts declares online that he's going to jump off of a building, and he'll die unless Superman saves him. Obviously, Superman does save him, but then the general public gets the perception that they own him now, and Superman has to prove that he's not just a tool that can be exploited and manipulated.
