Using Paragraphs

Wow!
I can already see the half confused half amused looks on your faces. 'Um Alice, we already know how to use paragraphs.'
Well, I thought I did too. I mean, we use them all the time in our writing. A few years ago, someone was looking at piece I wrote and said it needed to be broken up more. I should have started a new paragraph there, there, and there. I looked at it and thought I never learnt that in school. the more I thought about it though, the only thing I had learnt about paragraphs in school was to start a new one when a different character started talking.That can't be all there is to it. In short stories half the time no one talks and they have plenty of paragraphs. So, what are these other rules?
If you find an old piece of writing, say 'Dracula', or 'Mysterious Island', (a reprint of the original, not an adaptation) you might notice something curious about the way their paragraphs are set up. They're almost non-existent!
As far as I can tell authors of this time loved to info dump. This is where you write a long paragraph explaining everything in a very plain boring way. These days we are taught to show, not tell, which basically means a characters physical characteristics, personality, and back story, come out as we write, rather than our readers being told everything flatly, at the beginning.

In old stories you might get a paragraph explaining what an island looks like from the boat in great detail. Then another explaining where the boat landed in even greater detail. Then a character will spend two or three paragraph explaining to their companions how they got there and what they should do next. We're already here pages into the book! And I don't know about you, but I don't talk to anyone for three paragraphs before they respond (or occasionally to stop rambling).
These days we love blank space. Open up any recent book on your shelf, or a magazine or newspaper. Look! Paragraphs galore! These days, a rule of thumb is to try and have an almost even ratio or just under of white space to written words within a whole book.
But how do we know where to put all these extra paragraphs?
Well, besides the obvious when another character starts talking, you must remember that only one thing can be the subject of each paragraph. For example if I were writing about two characters it might go something like this:

Lucy wrapped her scarf around her neck, before heading out the door. Walking down the street she called out, "Hi Ben," as she passed him.
Ben looked down at his feet until she passed.
Lucy didn't seem to notice as she headed on her way.

In this Lucy is the subject of the first paragraph. It's all about what she is doing. She wraps a scarf round her neck, she heads out the door, and she says 'hi' to Ben.
Ben is in the next paragraph, and we switch paragraphs again, before talking more about Lucy.
This is the same for inanimate objects. If we look at the example I gave or an old book, the first paragraph is about the island. The second paragraph is about the part where the boat lands.
Hang on. Shouldn't they be in the same paragraph?

Well, no. The island as a whole can be one subject, but if you want to talk about just part of that whole, it's a different subject. For example, you might talk about a crowd of people in one paragraph, but you will need to start another paragraph to talk about an individual within that crowd.
Ideas can also be paragraph subjects, so each idea needs a new paragraph too.
Every individual thing needs its own paragraph.
Another way to use paragraphs is to help bring across the tone of your story. If you see a page with long paragraphs and not many breaks, it looks dark, and takes a long time to read. If your characters are depressed or moving slowly, this is perfect.
Alternatively, if you're writing a fight scene, there should be lots of short paragraphs. The action is happening fast so the readers eye should move quickly down the page. There might even be the occasional one word paragraph.
However, keep in mind that every section with long paragraphs should have a few short ones, and every section with short ones should have a couple of long ones to keep things balanced.