The narrator seeks out Simon Wheeler because the narrator's friend back East requested that the narrator find Simon and ask him about another guy, named Leonidas W. Smiley.

Presumably because the narrator is a good friend, he does what is asked of him, and looks for Simon so that he can ask about Leonidas and, hopefully, contact his friend back East to let him know that Leonidas is okay.

Of course, that's not exactly what happens in the story, though! The narrator does find Simon Wheeler, and he does ask him about Leonidas W. Smiley, but the narrator realizes just as we the readers do that his friend has played a joke on him. There is no such person as Leonidas W. Smiley, and his name, "Smiley," only reminds Simon about a long, boring story about a different guy with the same last name ("Jim Smiley") and Simon proceeds to tell this entire story to the narrator. The narrator is really annoyed and realizes that his friend probably planned out the whole interaction as a practical joke.

All this is reported within the very first paragraph of the story. It might be a little hard to understand, since it involves so many different men, so I'll also explain it like this. Here are the events in the order they happened, even though the narrator explains them all at once:

1. The narrator's friend asked the narrator to ask Simon Wheeler about Leonidas W. Smiley.

2. The narrator finds Simon and asks him about Leonidas.

3. Simon has idea who Leonidas is.

4. Leonidas's last name, "Smiley," reminds Simon of another guy, Jim Smiley.

5. Simon tells a long, silly, boring story about Jim Smiley to the narrator.

6. The narrator realizes his friend has tricked him by sending him on this errand--his friend probably knew Simon well and knew what would happen if someone mentioned the name "Smiley" to him.

Why does Simon Wheeler tell about the mare and the pup first, before focusing on the frog in "The Celebrated Jumping Frog of Calaveras County"?

There are two reasons Twain goes through Smiley's other modes of betting before getting to the famous frog of Calaveras County. The first is to provide the substance for the satire of the story. Besides being an amusing short story--unless one is of the same opinion as the button-holed inquirer after Reverend Leonidas W. Smiley--it is a satire upon the habit of betting in the West, or at least in Calaveras County. Satire is a jesting, ridiculing look at an element of a culture or an individual or a group of individuals for the purpose of exposing just how wrong-headed the behavior or individual or group is. In this case, Twain is satirizing those who are uneducated and who freely, incessantly bet.

Therefore, part of Twain's ploy in establishing an effective satire--the purpose of which is to inspire a change in the behavior or situation or individual(s)--is to make this type of betting appear to be as exaggerated and absurd as he possibly can. Consequently, he goes on and on and on about how Smiley would bet, "he'd change sides," and on what he would bet, "rat-tarriers, and chicken cocks, and tom- cats, ... till you couldn't rest," and about incidents of betting,

Parson Walker's wife laid very sick once, .... [He said] with the blessing of Providence, she'd get well yet; and Smiley, before he thought, says, "Well, I'll risk two- and-a-half that she don't, any way."

So the mare and the pup receive detailed telling yet are not the first to be highlighted. The list of which they are a part (as I can sort it out) includes betting on:

• horse-race,
• dog-fight,
• cat-fight,
• chicken-fight,
• two birds setting on a fence,
• Parson Walker at camp-meeting,
• straddle-bug (hypothetically),
• Parson Walker's sick wife,
• the fifteen-minute nag,
• a little small bull pup,
• and the frog

The other reason Twain gives details about the mare and the pup before getting to the frog is to establish characterization. Now, this is an odd point. Characterization isn't needed because Smiley undergoes any changes or epiphanies for which careful characterization is needed. Twain devotes all this attention to Smiley's characterization for two reasons: (1) to make the tale as "monotonous ... interminable ... absurd ..." as possible;

the monotonous narrative ... he never changed his voice from the gentle-flowing key to which he tuned the initial sentence [of] the interminable narrative ... such a queer yarn [told] without ever smiling, was exquisitely absurd ....

(2) to make his satirical points as emphatic as possible. In other words, had Twain jumped right in with Smiley getting straight to the frog incident, there would have been less effectiveness to the satire and there would have been less exasperated amusement at the whole amazing tale Smiley tells. By giving details on the mare and pup first, Twain fulfills his objects for writing the satirical story about betting on the frog of Calaveras County.