If you are writing the essay in proposal form, the form of "A Modest Proposal" is similar to typical proposal papers. Swift's narrator states the problem in an introduction: the problem of poverty. He then offers a solution. He follows it with justifications. He follows that with possible objections. Then he concludes by restating the useful effects of his proposal. The basic parts then are: introduction, solution, justification, objections to the solution, and a conclusion. The solution and justifications tend to be the bulk of the essay, but the introduction and objections can be long as well. Typically, the introduction and the conclusion are shorter sections but sometimes it takes a few paragraphs to fully state the problem in the introduction.
So, your thesis should be stated in your introduction and explained with the solution. If you are showing how "A Modest Proposal" is satire, this is part of the thesis. If you are offering a rebuttal to the satire (say that there are better ways of combating poverty than eating children, a good argument in any case), this should be the thesis. Likewise, a thesis could be used to show the similarities of satire in "A Modest Proposal" and "The Colbert Report." In each case, follow the form of a proposal paper with the basic parts.
As for an essay, it depends upon what you want to say. If it is an analysis of "A Modest Proposal" you should discuss the literary techniques of the essay itself: hyperbole (exaggeration), satire, and veiled or metaphoric critique of culture. Swift also uses a different persona as the narrator; it is not Swift himself. The narrator is being serious in his proposal to use children as commodities: food and clothing. But Swift is being satirical. Focus on this duality: Swift being satirical by using another persona/narrator to make this outrageous proposal.
Note also that this is a critique of the economics and culture of Ireland at the time, with particular criticism of England. Swift is being satirical by suggesting, via his narrator, that rather than addressing the oppressive system of taxing and manipulation of lands, that children be used to relieve the poor of their debts. His implication is that given the awful treatment of the poor by the ruling classes, it is not much of a stretch to suggest that their children be sold. The poor are treated so badly that this strategy won't be much different. The ruling class (and other classes) reap the benefits of the poor farmers; so they are already in a literal sense "eating" their products/offspring. This is all part of the satiric critique of the economic system. In other words, the narrator is playing the part of the oppressive, ruling class; using cold, heartless arguments to solve the problem of poverty.
Fourthly, the constant breeders, besides the gain of eight shillings sterling per annum by the sale of their children, will be rid of the charge of maintaining them after the first year.
If your essay is more than an analysis, perhaps you might compare it to an example of modern satire. "The Colbert Report" is a good example in this case because the host of the show is playing a character (just as Swift is playing a role as a narrator other than himself). And similar to Swift's narrator, the role Colbert plays is one who has strategic arguments but within the context of saying outrageous things. In the show, Colbert plays the role of an extreme conservative, one who holds the conservative ideology so dear that he willfully ignores the humanistic implications of the outrageous things he say. Just like Swift, his satire is clear because we know he is playing a role. And since the satire is clear, the listener/reader/viewer knows this is not just a satirical gesture for the purposes of laughter; it is also a strong critique of the types of people the narrator(Swift) and the host(Colbert) are satirizing.
i ment i need to write a proposal essay.