While we are often taught to begin writing an essay with the introduction, there is absolutely nothing wrong with writing an introduction last, and in many cases, that is the best thing to do! Since the introduction should draw the reader in, provide a little background information, and end with a thesis statement, we are often unable to put the introduction together until we know what is in the body of the paper. Let's talk about a few different approaches you can use for the introduction, and also, since I do not know whether or not you are expected to take a position on the death penalty, we should talk about that, too.
There are two primary ways to begin an introduction, first with what we call the funnel method, or second, by telling the reader a little story that lets the reader know what the subject of the essay is. The funnel method means beginning with a broad idea and then narrowing down to a specific thesis statement, just as a funnel is wide at the top and narrow at the bottom. So, for example, if I were writing a paper about trying juveniles as adults, I might begin by saying "There are many injustices in our legal system." This lets the reader know I am going to be discussing the legal system and some injustice in it, without being specific. Then I can narrow down to a statement or two about how we try juveniles as adults, perhaps adding a statistic on how often this happens, some information that would be helpful to the reader. I can then end the introduction with a thesis statement, and we will talk more about those below. We can tell a little story at the beginning of an introduction, too, so for my hypothetical essay, I might open with a description of a 15-year-old who has committed some foolish act that could result in his being tried as an adult. I might describe him sitting in jail, missing his parents. The idea would be to engage the reader and draw the reader in. Then I could ask a question, perhaps whether or not we want to be a society that does this to children. Finally, I could end with a thesis statement.
I do not know whether you are expected to be writing a paper that explains the pros and cons of the death penalty or are expected to take a position for or against the death penalty. These would result in very different kinds of thesis statements. For the first, you would make a general statement about there being pros and cons on this issue, and for the second, you would make an assertion that the death penalty was a good idea or a bad idea, and then you would state what points you are using in the essay to support your assertion. If I were writing a paper, for instance, on single-sex education and was just informing the reader about it, I might say something like this as my thesis statement:
Single-sex education has become controversial, but there are reasons it can be good for students, and there are reasons it can harm students.
The reader understands now that this is an informative essay, and I am going to explain the pros and cons without taking any position. But if I am expected to take a position on this issue, my thesis statement might look like this:
While there are some who oppose it, single-sex education can be beneficial for females and males, since females tend to be more assertive and intellectually adventurous when in a single-sex classroom, while males seem to thrive better without the distraction of females.
That is a thesis statement in which I am taking a position and listing the points I am going to discuss to support that position.
Which are you expected to write, an informative essay on the death penalty or an argumentative essay taking a position on the death penalty? Your introduction could be very much the same for either, using the funnel method or the story method, but your thesis statement will be different, depending on which kind of essay your assignment calls for.