A paragraph or three about paragraphing

In any essay longer than one paragraph, paragraphing is the decision to end the sentence mid-line, almost always to start a new block of writing (another paragraph) from a fresh line. The 'almost' in the last sentence is to accommodate the very last paragraph of the essay, to which the second half of the definition of paragraphing obviously doesn't apply. 

Now a paragraph performs certain well-defined functions. One, it may convey a new idea or a major development of an idea that has already been presented. Two, it may bridge distinct lines of reasoning, signalling a transition or shift from one way of thinking to another. Three, a paragraph (as in the case of the opening or closing of the essay) may have a strategic function. In the case of the essay opener, the goal is not only to situate the topic and plant the thesis but crucially to grab the attention of the reader. Similarly, the closing paragraph aims to wind the topic down to a graceful halt but also looks to leave a lingering appeal.

Indented, justified

Flush left, justified

In addition to being mindful of why you want to end one paragraph or start another, there are also a few simple tips about the mechanics of paragraphing.  If you are going to indent your paragraphs, indent all but the first paragraph. Try to keep the size of indentation consistent throughout the essay, say, the width of your forefinger. It is perfectly fine however to start all paragraphs, flush left. 'Justifying' i.e. writing within column borders on both sides of the page (as in a newspaper) is also a smart practice. And yes, leave one line blank between paragraphs. The upshot of all this advice is that paragraphing is intended to facilitate the reader. If you do it right, your essay will be easier to bite, chew and digest.