Deepak from Kanpur, India, asks the following question (edited for clarity):

In the sentence "I am a good writer," how does the meaning change based on which word you emphasize?

Well, Deepak, that's a great question! It turns out that you could say this sentence in several different ways, and each way of emphasizing the words gives a slight tweak to the meaning. To answer you, I'll mark the word that's emphasized by marking it off with asterisks. Beneath each sentence, I'll provide an explanation. In each case, the emphasis implies that the speaker is, in some way, disagreeing with what a previous speaker has said.

*I* am a good writer.
This sentence, with the emphasis on the subject, suggests that someone has previously made a statement implying that it was someone else who is a good writer. For example, if someone is comparing you to Mark, and says that Mark is a good writer, you would emphasize "I" to indicate that you're disagreeing with their conclusion is wrong about which of you is a good writer.

I *am* a good writer.
In this case, it's the verb you are emphasizing. What's the opposite of being a good writer? NOT being a good writer. So presumably, someone just told you that you are not a good writer, so you emphasize "am" in order to disagree with them.

I am *a* good writer.
Emphasizing an indefinite article like "a" is a strange choice under most circumstances, but I can imagine a circumstance where you might do that. You have just published your first novel, and an adoring (and maybe slightly crazy) fan says to you that you are "THE good writer." In other words, suggesting (hyperbolically) that you are the only good writer in the whole world. You disagree with that designation, and graciously point out to your fan that you are only one of many good writers.

I am a *good* writer.
Here you emphasized an adjective. So maybe someone just used a different adjective to describe your writing skills. Maybe they said, "You're a fantastic writer," and you wanted to dampen their enthusiasm by indicating that you're just good, but not fantastic. Or maybe they said you're a lousy writer, and you want to defend your skills by saying that you're a good writer.

I am a good *writer*.
In this case, it's likely that someone said that you're good at something else. Maybe they thought you illustrate children's books, when in reality you write them. Or maybe they thought you were a carpenter, but you're actually not. However, the fact that your sentence has the word "good" in it, suggests that the person speaking thought you were good at whatever it was that they thought you do. "You're a good illustrator." "No, I'm a good WRITER." 

And there you have it - a five word sentence, with five different ways of emphasizing the words! Each one has a slightly different meaning, because each one is a response to a slightly different situation. And if there is no surrounding context - if you were just announcing this into the silence - you probably wouldn't emphasize any of the words.