Bluff my way into the Watchtower so I could meet the entire Justice League, wait for J'onn J'onzz to be all, "you're not a superhero, wtf" and then turn on all the sheepish charm I could muster and admit I'm just a fanboy who wanted to meet the Justice League. With a little luck, they'll sigh and think it's cute and then I'll replace that obnoxious snapping motherfucker as their human mascot.
Or something.
Or maybe I'd just admit my non-superness to Wonder Woman at the get go and see where that goes. Basically, being talked to by Wonder Woman would be enough... XD
What would you do if a pair of Greek gods--say, oh, Zeus and Athena--descended from Olympus, both clearly irritated and fuming, and asked you to settle the dispute between them: Superman versus Goku?
(Keeping in mind that the Greek gods are notorious for being wrathful, vengeful, petty and jealous, so... XD)