Brain Storming, being the organic process that it is, doesn't have a right or wrong approach. Generally when you think of brain storming it's usually mentioned in tandem with writers block, like an anti-block pill that you swallow to ward off forced dialogue and such. It's a feeling every writer is familiar with so I came up with a few methods to help stave the syndrome.
The first is an exercise. (Like all exercises, you only get out of it what you put in. So if you go into it with apathy and a ho-hum spirit then maybe you should skip this step.) What I like to do is get a blank piece of paper, set a timer for 5 minutes and write down on the paper as many verbs as I can think of until the timer ends. Afterwards, take all those verbs you wrote and set the time again for ten minutes. The goal is to write a short story using only the verbs you wrote down within the time limit. The story could be as silly or serious as you'd like. It doesn't matter. As long as you are writing some kind of narrative you will have succeeded in the exercise.
Now the point of the first exercise is two fold. First, it's important that you are just in the habit of writing. That goes without saying. Just like any hobby, be it art, music, sports etc. you must maintain a practice regimen if you want to get better. They say that in order to get better at anything, and eventually master it, you have to put in about 10,000 hours of practice. Once you're there you'll be pretty damn good I'm certain. That being said, the second purpose of the exercise is to get you writing under a deadline. There needs to be an urgency while writing, as if what you're trying to say is pertinent to the salvation of the entire world. I say it like that because everybody writes for a reason. Every article you've ever read was written by someone passionate about that topic, and you should be about yours. Therefore writing under a deadline will train you to take this process seriously and eventually you'll be producing great material.
The second method I use to help brain storm is largely creative and a little stranger. It's always worked for me, which may or may not be helpful to you, but I stand by it's success. I often find myself making stories all the time, but generally from silly, diametrically opposed things or people. For instance, I once thought about writing a short story about a mangy eighties metal guitarist moving in with his aunt, a southern baptist quilter. It sounds like an awful idea, but it allowed my mind to move on to a better, much more sophisticated one. Another start-up idea I had was about an anthropomorphic Galapagos tortoise who doubled as a secret agent, only he wasn't good at his job, at all. He was awful, and happened to only save the day through circumstance. I had a similar idea involving a co-worker I work with who is this old dishwasher in his fifties, and batshit insane. And I thought about turning him into this government agent building this elaborate cover of being this awful human being. I just thought it was funny, but what it did for me on a more substantial level was give me access to a bunch of other ideas. Essentially this second option is really about keeping your brain switched on. If you never turn it off, something in there is bound to come out eventually.
The third and final brain storming method I've always used is keeping a book regimen, a book you read once a week, and just keep at it. Four books a month, forty-eight books a year. First you'll get ideas from other authors, or at least varying takes, but what you'll also get is their styles and varying approaches to narrative. Generally what I like to do, is if I find a really good author, I take a page of their book and copy it word for word into a word processor. This forces you to enter their writing style and kind of experience what it must have felt to write that particular page. It's a very fun way to involve yourself into the stories of your favorite writers too. My favorites are Neil Gaiman and Grant Morrison. They have really experimental styles and introspective dialogues, which are great for getting the interior psyche of a character on the page. If you're up to it, copying by hand will help as well, slowing down the pace and really fleshing everything out.
Those are kind of guidelines I generally follow. I hope they make for some great stories. Happy writing!
PS: Next week I'm going to start a short story series. Tell your friends and check it out if you can!