Most writers clearly state a problem to introduce a persuasive essay. Once in a while, to set the tone and quickly engage the reader, the writer will open with a little story or some compelling statistics. If so, the formal opening statement follows in the next paragraph. It generally should not extend past one paragraph. At the end of the introduction or at the beginning of the next paragraph, the writer makes a one-sentence arguable statement, commonly called a thesis. The thesis is the focal point of the essay, and everything that follows should relate to it.
To help readers understand the scope of the problem, a good writer will next more fully explain the problem stated in the first paragraph, paying particular attention to why the problem matters, and explaining what the consequences will be if it continues. This section may include data, statistics and other credible information to support the writer's contention. It may be short or quite long.
Anticipating and rebutting objections and counter-arguments is critically important in most argumentative essays. The optimal place to do this is after you have established the extent of the problem, although some writers reverse the order and propose solutions first and then address counter-arguments. There is no rule about which way to do it, but discussing solutions later in the essay leads to something resembling a climax. The rebuttal section should be as long as it needs to be to fairly discuss counter-arguments.
In this section of the essay, the writer proposes and explains solutions or a new way of thinking about the problem. Often more than one solution might solve a problem. If so, the writer will touch on the most important of them, but then explain why his solution is the best solution, including any benefits that will come of it. Feasibility is an important consideration in this part of the essay. It's not enough to propose a solution without also addressing whether it can be feasibly put into action. Most writers devote a good amount of space to this section. Finally, the conclusion follows from or is part of the last section. It may take the form of a summary or it might echo the beginning, particularly if the writer opened with an anecdote or statistics.