The following information comes from: http://bellevuecollege.edu/asc/writing/essays-guides/documents/paragraphtransitions.pdf and http://owl.english.purdue.edu/owl/resource/606/01/
Elements of a Paragraph
To be as effective as possible, a paragraph should contain each of the following: Unity, a topic sentence and a good transition between paragraphs.
Unity: The entire paragraph should concern itself with a single focus. If it begins with a one focus or major point of discussion, it should not end with another or wander within different ideas.
A topic sentence: A topic sentence is a sentence that indicates in a general way what idea or thesis the paragraph is going to deal with. Although not all paragraphs have clear-cut topic sentences, and despite the fact that topic sentences can occur anywhere in the paragraph (as the first sentence, the last sentence, or somewhere in the middle), an easy way to make sure your reader understands the topic of the paragraph is to put your topic sentence near the beginning of the paragraph. (This is a good general rule for less experienced writers, although it is not the only way to do it). Regardless of whether you include an explicit topic sentence or not, you should be able to easily summarize what the paragraph is about.
Smooth paragraph transitions help readers move from the last paragraph’s discussion to a new paragraph’s ideas.
To build an effective paragraph transition, a writer has to show the reason that one paragraph comes after another, just as a sentence can usually make sense only because of the sentence before it. (Imagine how confused you’d be if the passage from below first sentence weren’t said):
Eating a tart cherry pie has always made my mouth water. Sometimes I drool so much that red juice runs down my chin. A waitperson at a restaurant even remarked to me once that I appeared to be in a pie-eating contest with myself.
Answer the following question: What words and ideas reoccur to connect the sentences? What do you think the next paragraph will be about and why?
The first and second sentences use the synonyms salivate and drool. The characteristic red color of cherries mentioned in the second sentence connects it to the first. The last sentence connects to the topic sentence by repeating the word pie, and it connects with the second sentence with the idea of being messy. These synonyms, repetitions, and common ideas help to create paragraph cohesion.
The paragraph left off with a stranger making a comment about how sloppy a pie-eater the speaker is. In general, a new paragraph is started when a different topic,time, or place is being discussed, so right away the reader will expect something different—but related—to be discussed when a new paragraph begins:
Here is where the last paragraph left off….
. . . at a restaurant even remarked to me once that I appeared to be in a pie-eating contest with myself.
Here is the second paragraph
I frequently find myself the recipient of personal comments bestowed by who may imagine they are being helpful or at least funny. I always try to have a sense of humor and humility about myself, but self-deprecating humor is my preferred way to connect with others. Suddenly having a person leap out and make a joke at my expense only pains my all-too-thin skin.
The second paragraph becomes a broader discussion of the type of behavior the author has experienced from strangers. The new paragraph’s topic sentence refers back to an unfamiliar person’s humorous actions but its purpose is to expand the scope of the topic to include the effects of this type of situation. Though the second paragraph has a new focus, it first rewords and builds on the ideas of the previous paragraph in order to carry the reader toward a new area of thought.