Paragraphs represent the basic unit of composition: one idea, one paragraph. However, to present a clear, unified train of thought to your readers, you must make sure each paragraph follows the one before it and leads to the one after it through clear, logical transitions. Keep in mind that adequate transitions cannot simply be added to the essay without planning.  Without a good reason for the sequence of your paragraphs, no transition will help you.  Transitions can be made with particular words and phrases created for that purpose--conjunctive adverbs and transitional phrases--or they can be implied through a conceptual link.

Conjunctive Adverbs and Transitional Phrases

Conjunctive adverbs modify entire sentences in order to relate them to preceding sentences or paragraphs; good academic writers use many of them, but not so many that they overload the page. Here is a list of some of them, courtesy of The Brief Holt Handbook:
 

accordingly  also anyway besides certainly consequently finally furthermore hence however incidentally  indeed instead likewise

meanwhile moreover nevertheless next  nonetheless now otherwise similarly still then thereafter therefore thus undoubtedly

Transitional phrases can perform the same function:
 

in addition in contrast for example for instance

of course as a result  in other words as a result

Use them wisely and sparingly, and never use one without knowing its precise meaning.

Implied or Conceptual Transitions

Not every paragraph transition requires a conjunctive adverb or transitional phrase; often, your logic will appear through a word or concept common to the last sentence of the preceding paragraph and the topic sentence of the following paragraph. For example, the end of a paragraph by Bruce Catton uses a demonstrative adjective, "these," to modify the subject of the topic sentence so that it will refer to a noun in the last sentence of the preceding paragraph:

When Ulysses S. Grant and Robert E. Lee met in the parlor of a modest house at Appomattox Court House, Virginia,...a great chapter in American life came to a close.

    These men were bringing the Civil War to its virtual finish.

What I did not know when I began researching the connection between radioactivity and genetic damage was that I would find the probably cause of my own family's battle with cancer and other health problems.

    Hailing from Utah, the state known for its Mormon population's healthy lifestyle, my family has been plagued with a number of seemingly unrelated health problems.

Paragraph transitions can expand the range of discussion as well as narrow it with an example, as Quintana's transition does; this selection from an article by Deborah Cramer on the ecological impact of the fishing industry shows how a single instance of overfishing indicates a world-wide problem:

....The large yearly catches, peaking at 130 million pounds from the Gulf of Maine in 1942, wiped out the fishery.  It has yet to recover.

    The propensity to ravage the sea is by no means unique to New England.  The northern cod fishery in Canada is closed indefinitely.  In Newfoundland more than 20,000 fishermen and fish processors were abruptly put out of work in 1992 when the government shut down the Grand Banks...

Proofreading Paragraph Transitions

At some point in your editing process, look at the end of each paragraph and see how it connects to the first sentence of the paragraph following it.  If the connection seems missing or strained, improve the transition by clarifying your logic or rearranging the paragraphs.  Often, the best solution is cutting out a paragraph altogether, and replacing it with the right one.