speaker is in a sleigh pulled by a horse in a lovely countryside blanketed in snow. Apparently, he is cutting through someone's woods on his way, and moved by the beauty of the "woods and frozen lake,...easy wind and downy flake," he stops to revel in the beauty of the natural scene. But, the horse shakes his harness bells which act as a reminder to the speaker that he has obligations and must continue his journey. 

• What is the conflict for each speaker?

"The Road Not Taken"

1. Literally, the speaker regrets not having gone down a less-traveled path which may have proven more interesting than the one he did choose. With reference to Frost and his friend Edward Thomas, they both enjoyed the flora and fauna of the areas in which they trekked, and Thomas always worried that he could have missed certain flowers, etc.
2. Figuratively, the speaker may ruefully recall his having chosen the path less traveled because he has lost a wonderful opportunity which could have been very rewarding to him personally.

"Stopping By a Woods On a Snowy Evening"

1. Literally, the speaker who drives a horse-drawn sleigh across the countryside on a beautiful snowy evening in a wooded area, desires to pause and enjoy the natural beauty of the setting: "The woods are lovely, dark and deep." However, his horse's bells remind him that he has miles to travel before arriving home.
2. Figuratively, the speaker wishes to pause and enjoy the respite that the open area away from civilization affords him. In this lovely woods, he finds that he can relax his troubled spirit by contemplating the beauty of Nature in a transcendental moment. However, his reverie is interrupted by the harness bells that remind him of the hour and the fact that he has worldly obligations and much to do yet before he can rest: "miles to go before I sleep."

• How does each speaker resolve his conflict?

"The Road Not Taken"

The speaker does not resolve his conflict; instead, he mulls over the experience in the woods, suggesting that he wishes he had the choice to make again. "If only I had" must resonate in his mind because he states with regret,

I shall be telling this with a sigh
Somewhere ages and ages hence:...
I took the one less traveled by,
And that has made all the difference.

"Stopping By a Woods On a Snowy Evening"

The speaker resolves his conflict by recommencing his journey. His sense of personal responsibility motivates him to move on because he realizes, although with some regret it seems, that he has "miles to go before...sleep."

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Re: The essay

As per instructions, be sure to use your own words, but the first paragraph written above can be paraphrased as part of your introduction. Then, as the final sentence of the introduction, write the thesis statement. This thesis statement could, for instance, contain a general statement about the act of reflection in both poems. Here is an example of a thesis statement (You will need to create your own to avoid plagiarism):

• Example of a Thesis Statement:

Both "The Road Not Taken" and "Stopping By a Woods on a Snowy Evening" by Robert Frost are reflective poems that emphasize the importance of single moments in the lifetime of an individual as such moments demand choices, decisions, and obligations that profoundly affect one's life.

• Body of the Essay

The body of the essay then develops the "blueprint" given in the thesis statement; that is, the 3 topic sentences can be statements about (1) choices, (2) decisions and (3) obligations--or whatever 3 you decide upon. These 3 topic sentences begin each paragraph of the body of the essay and are supported with the lines of the poem and the literary devices discussed in your previous question:

http://www.enotes.com/homework-help/important-note-individual-work-express-your-own-474247#answer-674229

• Conclusion

The conclusion is little more than a rewording of the thesis statement, along with a relevant observation that leaves no doubt in the reader's mind that the essay is finished. Perhaps you could write a statement about the fact that people's characters are, indeed, formed by the decisions they make. 

Re: APA style. It is surprising that your teacher desires this type of documentation as writing about literary works is customarily formatted with MLA style. However, you should follow instructions; so, you can access APA by going to the Purdue website in the links below.

In "The Road Not Taken" by Robert Frost, the traveller is faced with a decision- to take the well travelled path, or to take the one less taken.... often seen as the metaphor for forging your own path, being an individual, rather than following a seemingly "normal" path in life.

The conflict thus begins.  He chooses the path less taken.

Then took the other, as just as fair,
And having perhaps the better claim,
Because it was grassy and wanted wear;
Though as for that the passing there
Had worn them really about the same,

Oh, I kept the first for another day! Yet knowing how way leads on to way, I doubted if I should ever come back.