What makes a good introduction to a persuasive essay?

There are two different strategies that I find helpful in introducing a persuasive essay. First is to provide a striking fact. Second is to provide a striking anecdote.  In either case, it is necessary to write a thesis statement at the end of the introduction, to let the reader know what you are trying to persuade them about, along with your supporting points. 

Let's suppose I want to persuade my readers to vote. I might begin with a statistic, like this:

Only 10% of the people who are eligible to vote elect our nation's leaders.

I don't know if that is a fact, but for the sake of this discussion, let's assume it is.  I am counting on my reader to find that a shocking fact, and then I can build on that fact throughout the introduction, perhaps like this:

Only 10% of the people who are eligible to vote elect our nation's leaders. This means that a very small minority of people is weighing in on who should be in charge of the country.  This does not seem like a desirable state of affairs, when our leaders' actions and decisions affect 100% of the country.  Everyone should vote, to have a voice in the direction of the country, to exercise a right that people have died for, and to perform a civic responsibility. 

I have opened with a shocking statistic and then explained its implications, making clear I do not find them good ones. I end with a thesis statement, what I want to persuade my reader to do, along with three good reasons to do so.  This is one strategy that can be used to introduce a persuasive essay.

An anecdote is just a little story, a vignette that you can open with, to get the reader's attention with a bit of drama.  If I were writing a persuasive essay about amnesty for unlawful immigrants, I could begin with this:

The little Latina girl sobs as her parents are led away by federal officers.  The parents' faces are frozen in grief, as they are taken back to Mexico, to a life without their child.  This is the state of immigration today. 

From there, I could go on to discuss immigration a bit, finally ending in a thesis statement, urging my readers to support amnesty, along with at least a few good reasons for doing so. 

In a persuasive essay, in addition to using logic or ethics to make your case, you can appeal to the emotions of your reader, using what we call pathos. And certainly, if you can use that at the very beginning, you are getting off to a great start.