What would be an effective introduction for an essay on one's personal Utopia?
The word "utopia" literally means "no place" because it represents a perfect ideal which can never be met here on earth--or at least as long as humans are inhabiting earth. It is just not possible to have a perfect place because it will always be inhabited by imperfect people. Utopianism was a popular form of writing and thinking in the nineteenth century.
[T]he utopian tradition flourished as writers sought to dramatize the political and economic principals—equality, freedom, and material plenitude among them—necessary for the advancement of society. Likewise, a number of real-life experiments were undertaken in the form of contained, usually short-lived, utopian communities designed to test the viability of a fully cooperative society where competition and want were unknown.
This movement was eventually replaced by dystopian literature, in which authors believed nothing positive would ever happen again due to governmental or authoritarian oppression.
I am making the assumption that you have been asked to write an essay in which you describe your utopia, your perfect place, and that you have already determined what elements a world might need to have to be perfect in your eyes. An introduction should set the tone for the rest of the essay, should preview your key points (in the form of a thesis or purpose statement), and should capture your readers' interest.
Though it is likely that your particular audience already knows about the meaning of "utopia," that is one way you might start your essay. Another is to select one of many, many quotes on utopias or dystopias (because one way to define something is by telling your readers what it is not); just be sure the quote is directly applicable and is not simply a distraction for your readers. You might also create a kind of frivolous or "cheesy" utopia to start with, like something a five-year-old might describe: candy growing on trees, money everywhere, no chores to do--ever. While these can be considered perfect, they are rather superficial; from them you can move to some more important and significant ideas which you think would make the world a better, if not a perfect, place. Perhaps you could give some examples of what people in a few key ages groups (toddlers, teenagers, oldsters) might want in a perfect world (candy, sleep, health) and then, again, move to something more substantive.
Whatever you choose to use as an introduction should move to your key points smoothly, without getting off track or taking your readers down a path that is only superficially connected to your actual essay. Happy writing!