The way the character of Simon Wheeler is developed is primarily through the tone that Twain has him recount his hilarious "tall tale" about the aforementioned frog. Note what the narrator tells us about his method of storytelling:
Simon Wheeler backed me into a corner and blockaded me there with his chair and then sat me down and reeled of the monotonous narrative which follows this paragraph. He never smiled, he never frowned, he never changed his voice from the gentle-flowing key to which he tuned the initial sentence, he never betrayed the slightest suspicion of enthusiasm; but all through the interminable narrative there ran a vein of impressive earnestness and sincerity, which showed me plainly that so far from his imagining that there was anything ridiculous or funny about this story, he regarded it as a really important matter and admired its two heroes as men of transcendent genius in finesse.
The best comedians of course are able to deliver their most hilarious lines with a completely straight face. The contrast between their solemn manner and the absurdity of their material adds greatly to the humour, and this is precisely how Twain develops the character of Simon Wheeler as a great stand-up comic. So, Twain primarily develops the character of Simon Wheeler through quickly making it clear that he is a master storyteller and incredibly funny.