One way to stimulate brainstorming is to put basic ideas on slips of paper and put these slips in hats or a basket or anything for drawing from. In one hat, put in slips with occupations written on them. In another, put in hobbies. In a third, put in situations. And in a fourth, put in events or settings. Now draw a slip from each of these hats and using that information, brainstorm an idea for a story.
One of the key elements of brainstorming is to try out alternate paths for every action and determine which path is the most exciting from a literary standpoint. To facilitate this, use a flowchart design. Start with the first plot point or event, placing the information in a box. From this box, draw lines radiating outward, each terminating with another box. In those boxes, place different reactions to the first plot point, different ways in which the characters could go, storywise. From each of these boxes, continue with the different possibilities.
This brainstorming technique requires multiple participants. Take a starting idea and go around in a circle with each person adding one new element or twist to it. Someone will need to record all the ideas in case someone down the line has forgotten part of it. Go around and around, throwing out ideas. Periodically, go through the additions and cull out those that don't work as well to narrow down the focus. Keep the round robin going for as long as it takes to fully work out the idea.
This technique can be employed by oneself or with the help of others. Writing is all about "what if?" So use that to stimulate brainstorming. Remember in brainstorming you're seeking new directions to take, so let the ideas be extreme and even improbable. Don't edit them just yet. Sometimes, from something wild comes the perfect idea. Start with an opening scene and ask yourself, "What if this happens next?" Who knows what you'll come up with.