My personal brainstorming strategy usually involves going for a long walk (or run or hike). I like to play through scenes in my head and will jot things down on my phone if I get an idea I like. It's a little harder for me to sit down and try to actively brainstorm, at least for major scenes. I tend to plot things by the emotional beats of the story, and music can be good inspiration there.
Listening to a lot of Florence and the Machine while on a run isn't exactly a brainstorming strategy that works for everyone though. For actually sitting down to brainstorm, I like to write down first the plot events that I'm pretty happy with, in chronological order. Then I write down ones I'm not sure about or just random possibilities. I'll check out my notes on my phone to see if there are any ideas I wrote down that might fit in well.
From there, if I have a plot idea that I like, I think about how it would fit in with the other ideas. I'll usually think about it multiple different ways; like what does it mean if the character wins this fight, what does it mean if they lose, and does the story lose anything if I don't include this scene? I like the idea of index cards as well- if you have a lot of scenes already figured out, it can be nice to see those as a timeline and play with rearranging things.
