Generally, a paragraph should cover one topic. When the topic switches, a new paragraph should begin. Here's a non-fiction example:Over a billion people in the world live in extreme poverty. These people often have to eat on very little money; often their income (adjusted to US money) is as little as $1.50 per day. With so little money, choices are few, and they often subsist on cheap grains, with very little meat or produce.
Live Below the Line is an organization that seeks to educate people about the problem of extreme poverty. From April 28 - May 2, several thousand people are voluntarily eating on $1.50 per day, in order to better understand the problems faced by the poor. These volunteers seek sponsorships; the money will go toward any of several of the most reliable charities for hunger relief.
You can visit my Living Below the Line page here. All of the money that I'm raising will go toward The Heifer Project, an organization that provides livestock to poor families, both as a source of food and of income.
You'll see that the first paragraph is a general informational paragraph on the topic of eating on extreme poverty. The second paragraph changes topics, and covers the work of an anti-hunger organization. The third paragraph covers my own fund-raising efforts.
It's a little bit different when writing fiction. You still need to limit paragraphs to one topic, but you also have to switch paragraphs every time a new person speaks, or every time a new action occurs. Paragraphs in fiction may be very short--perhaps only a few words--or quite lengthy. Here's an example from fiction (I've numbered the paragraphs to refer to them later):1. It was a long train ride from Boston to Savannah, and Beau and I hadn’t bought sleeper tickets. When night fell, he covered me with his suit jacket and we dozed a bit, my head on his shoulder.
2. Early in the morning, we rattled into Savannah station; Beau’s mother sent a car to meet us there. My linen dress, the color of fresh butter, had wrinkled. I tried in vain to smooth it out—it was the dress I’d worn to marry Beau a month earlier.
3. I’d not intended to ever go south again. My mother’s rigid back and my sister’s tears were the last sights I’d expected to see through Georgia’s haze. Apparently, however, one does not ignore a summons from Mrs. Beauregard Montgomery, especially one that will probably be her last.
4. She was seated in the parlor, a yellowing lacy shawl around her shoulders and a quilt on her lap. Behind her, a set of crossed Confederate swords—her grandfather’s—were mounted above the fireplace. Vases everywhere were filled with lemony lady’s-slippers. Beau knelt beside her chair, grasping her hand in both of his. “Mother,” he said. Then again, “Mother…” I stood at the doorway, silent.
5. She touched his cheek, then chastised him in a wavering voice. “Where are your manners, junior? Tell your bride to come closer. I want to look at her.”
6. Beau beckoned me over and I approached her, my heart in my throat. “Mrs. Montgomery, I’m…I’m pleased to meet you.” I offered her my gloved hand, and she pulled me closer. Her eyes held mine, then she reached up and fingered an escaped ringlet, damp with Georgia air.
7. She didn’t speak for an eternity. Then—“What did you say your name is?”
Each paragraph has its own separate theme or purpose:
1. Introduction of two main characters and the setting
2. They change locations
3. Slight flashback, character building
4. A new character is introduced
5. One character's dialogue
6. Another character's dialogue and actions
7. Another character's dialogue and actions
Notice that the paragraphs are of several different lengths.
In non-fiction, paragraphs tend to have more than one sentence, and there is often a topic sentence, or a sentence containing transition from the previous one. Those transitions are particularly important (and there is a lesson in the forums on writing transitions here
). However, there is no rule, either in fiction or in nonfiction, about the number of sentences in a paragraph.
I hope this helps, and please let me know if you have further questions!