Overall, most of the characters in "The Celebrated Jumping Frog of Calaveras County" are not painted in a very flattering light.  The characters demonstrate ignorance, laziness, an addiction to gambling, cheating, lying, and general annoyingness all around.  Even the chatty Simon Wheeler, who narrates the story, and is of a more current time period in the west, is portrayed as overly talkative and highly irritating.

Twain, in his zeal for satirizing characters, takes it to its full extent in this story.  Twain loved to satire interesting and bizarre people that he met on his journeys across the nation, and to do that, he made fun of them by exaggerating their traits and painting them in unflattering lights.  In his journeys, he no doubt ran across a lot of men much like Wheeler and Smiley, who, when they weren't fortune-hunting for gold or mining, sat around gossiping, gambling, betting, and playing other games to pass the time.  And, in a lot of the gold rushes, those things did in fact occur.  It was a rough time in history, a time that was filled with huge masses of men descending on areas, bringing with them a lot of rough, uncivilized ways.  It was an interesting environment, one that is a part of our history, even if it was unsavory and rough around the edges.  Twain used his talent at satire to paint a colorful picture of these people as he might have found them.  I hope that helped; good luck!

In "The Celebrated Jumping Frog of Calaveras County," how does the author present the conflict between East and West?

To me, the conflict between East and West is presented by the predicament that the narrator finds himself in.

While it is not said that he is an Easterner, he is at least acting on behalf of a friend from the East when he asks Simon Wheeler about Leonidas Smiley.

Once the narrator starts talking to (perhaps I should say listening to) Wheeler, we see the conflict.  The narrator represents the East -- he wants to get down to business and be serious.  Wheeler represents the West with his uncouth manners and tall tales.

Figuratively, the West torments the East with all the tall tales, driving the East to, essentially, run away to avoid having to hear more.