theme and O Henry's reason for writing the story may not be the same.  If you can distinguish between the two it will add to your response.  

2) What are the strengths of "The Ransom of Red Chief"?

This story came out in the Saturday Evening Post, a very popular magazine at the time.  Hundreds of stories like this one were published in its pages over the years.  Why did this story become a classic?  

• Ask yourself, what makes this story memorable?  Why would other authors throughout modern history use this plot again in their stories? (It's been used in productions from major movies to My Little Pony episodes.)  What makes it uniquely entertaining?  
• Think about the switch at the end of the story.  M. Night Shyamalan (Sixth Sense) as a director loves to employ the switch at the end that made O. Henry famous.  Why do people like this type of slight of hand in the stories they watch or read?
• Think about the characters: How are Sam and Bill's characters likable even though they are kidnapping a child?  How is Johnny both likable and unlikable?  What about his father, who ends up getting the last laugh in the end?  Is he a likable character?  Why?  Now, once you've looked at the characters with this perspective, is this one of the reasons that this story is a classic?  How important are memorable characters?
• Think about the way the story is told.  Sam is the narrator of the story.  How is his voice different than the other characters'? Ask yourself: What if the story was told from Bill's perspective?  How would he have explained what happened?  What if the story was told from Johnny's perspective?  How would it be different from the story Sam delivers?  Last: What if there was a third person narrator (not someone actually involved in the story)? Would the story be as interesting if you weren't getting Sam's reactions and perspective?  
• Next, go through the story and look at the size of the paragraphs.  In general, short paragraphs speed up the story and longer paragraphs slow down the story.  The same is true for sentences.  How did O Henry use this writing technique to his advantage in this story?  Where are the longer paragraphs?  What do the paragraphs look like at the end of the story?  Or is the format of the story a problem?  Where are there big issues with the way the story was written?
• Think of the use of dialogue.  How does the interaction between characters add to the story?  Since it is a short story, O Henry had to be very specific about what each character says.  There is no room in a short story for a pointless piece of dialogue.  What makes this dialogue successful?  Is there anything unsuccessful or distracting about the dialogue?
• Now ask yourself: Could O Henry have done it better?  It is a daunting question, because he is the author you are studying, but you are the reader and your opinion is going to be important to this paper.  Thinking about all of these questions, could O Henry have written it better?  If so, how?  In considering this, think about writers today.  Would they have written this story the same?  Why or why not?  (You are considering the plot and characters in this question, not necessarily the lack of modern jargon and slang.)  Would the story have to have more action today, stronger characters today, or a different plot today to be considered entertaining?

Now that you've thought through the piece, it's time to organize your paper.

The first thing you need to write is your thesis.  Remember, you are writing a first draft.  As you write your paper, you may change your thesis as you think through the story.  It is perfectly fine to change your thesis while you are in the rough draft phase.  For now, write a paragraph (3-5 sentences) summarizing what you considered in the above questions.  Don't go into a great deal of detail by providing examples.  This will come later in your paper.  

Once you have written your thesis statement, the next section of the paper should be a short summary of the story. Keep it simple.  You should also give a brief background about O Henry.  I'm including a bio in the reference links below, where you can find out more about him.  Keep in mind when you are writing about O Henry that he was indicted for embezzlement and had to leave the country to go to Honduras.  (Bill and Sam are sympathetic for a reason.)  

The next section of your paper is the analysis of the story.  Here is where we return to the questions I gave you at the beginning of this post.  Simply go through each of those sections and write what you thought.  Use examples from the story to back up what you are saying.  Make sure to spend time on each of the points you make in your thesis.  (When you are done with this section of the paper, go back and review your thesis to make sure they match up.)  

The last section of your paper is the reaction section.  This is where you get to say "I liked it" or "I didn't like it."  If you have said that earlier in the paper, go back and remove it, unless it is in your thesis.  (Even then, it's better to wait.)   In this section explain why you like or didn't like the story.  If you have trouble doing this, ask: What has happened in my life or what hasn't happened in my life that makes me like or hate this story?  If you have specific experiences, share them.  Think about what made you interested in this story or what distracted you. Does this story remind you of any other stories that you have read?  

The final section is your conclusion.  In general you are going to restate your thesis; however, this time adding your own opinions about the story is an excellent idea.  Make sure the final sentence is the thing you want the teacher/professor to think about in regard to this story.