The paragraph is the unit of prose composition.* It usually consists of at least six sentences and no more than two-hundred words. It makes a single, well-defined claim and supports it. The claim should be articulated in a relatively simple, declarative sentence somewhere in the paragraph. We call this the key sentence. The rest of the sentences are organized around it, beneath it, or up to it.
A paragraph is a very limited statement of what you know. It is the scholar's task to divide the known into discrete, articulable units, each of which can be stated and supported on its own. So training your ability to write paragraphs is tantamount to organizing your knowledge in a scholarly way. It allows for one's ideas to be examined one at a time by one's peers.
I wonder if I'm a mystic about this. The zen master does not offer much in the way of technique, but is very stern about discipline. You must sit down, hold your hands just so, etc. But then you must simply sit and "be" (perhaps counting your breaths) for half an hour. I'd prefer to take this line on what a paragraph is. A paragraph is what you write for twenty-seven minutes when you are trying to say exactly one thing, using at least six sentences and at most two-hundred words. Every time you try to do this you learn something about what it is you're trying to do, i.e., what a paragraph is.
No amount of "technique", principles, rules or "elements of style", will get you around the basic need to practice. Writing forty paragraphs this way will take you twenty hours. I simply can't think of a better way to spend twenty hours learning what that might teach you.
If you want more detailed instructions try this post: "What to Do."
*This statement may need some qualification. It can be argued that prose consists of sentences, and that a text does not need to be composed into paragraphs to qualify as prose. I've dealt with this concern in a post on prose and poetry, but let me say something here too. If a series of sentences, each separated by hard line returns, is to count as "prose", then I would insist that they are each one-sentence paragraphs. That is, a case must be made that each sentence both states and supports its thesis, perhaps by appealing to something in the context. If not, the sentences come to stand, precisely, unsupported. And that's what makes them fail the test of prose. They may still be beautiful, and even useful. Certainly, they may be meaningful. They just aren't a prose composition.