During the first paragraph of the analytical essay, writers must present the thesis, which is the major argument the essay revolves around. You may argue that Abraham Lincoln was the most successful President in the history of the U.S. as he guided the country through a national crisis, or that biofuels is not the answer to the energy crisis because they are not as efficient as conventional fuels. Whatever your thesis, it must be clear to readers, who should understand from the introduction what the essay -- and the writer's perspective -- is about.
The main section of the essay must contain at least two paragraphs, with an obvious beginning, middle and end. The opening sentence of each paragraph must show how the materials of the paragraph relate to the thesis. This way you avoid entering irrelevant information and help your audience understand the importance of each paragraph. The information you include in each paragraph must be based on logic, evidence and analysis, and not on personal interpretations.
Another element analytical essay writers must be aware of is smooth transition from one paragraph to another. This is possible with a short sentence at the end of each paragraph acting as a prelude to the next. For example, after mentioning biofuels' difficulty in extraction, you can write, "However, this is not the only drawback of using biofuels with the current technology." Transition sentences help you keep a smooth structure, linking every paragraph with each other and the thesis.
The concluding paragraph must not just reiterate the thesis, but enhance it based on new knowledge acquired by reading the main section of the essay. For example, write, "As technology to extract biofuels is still costly, and even the final product is not as efficient as petrol, biofuels is not the immediate answer to the energy crisis." Furthermore, the conclusion of an analytical essay is not the place to bring new ideas or leave ambiguous remarks.