There is both direct and indirect characterization of Smiley.
Direct characterization is when the narrator tells the reader a character’s traits. Indirect characterization is when the reader infers a character’s traits from the character’s actions, what the character says, other characters’ reactions to the character, and what other characters say about the character.
At the beginning of the story, the narrator says he suspects Smiley is a myth but is going to report on his friend’s story anyway. Twain tells us he is reporting “the history of the enterprising vagabond Jim Smiley.”
Smiley is directly characterized by Simon Wheeler’s description of him. We learn that he was “the curiosest man about” and loved to bet, and he was also “uncommon lucky.” He would apparently bet on anything, and sometimes was rich and sometimes not.
Why, it never made no difference to him he would bet on any thing the dangdest feller.
These statements describe who Smiley is from the second narrator Simon Wheeler’s perspective.
There is also indirect characterization of Smiley through his actions. For example, Smiley keeps a horse that has asthma and is very slow. He still races the horse, and she wins because she gets desperate when she thinks she is losing. This demonstrates that Smiley is wily, but also that he gives others’ a chance and likes to defeat perceptions.
Both of these attitudes are clear in the frog contest.
Smiley said all a frog wanted was education, and he could do most any thing and I believe him.
In the end, Smiley bets that his frog can outjump any frog. The spectacle created is a logical outgrowth of both the direct and indirect character traits developed in the story.