So, I put my fingers on my keyboard, and words come out. Sometimes those words are even in English!
Taking tongue out of cheek for a moment, if I had to describe the quirks of my process, they would be:
Outlining. Pretty much every longer work I've ever created started with an outline, and the stories and characters come to life at this stage. If you read Re:Apotheosis, the process Kaguyama describes in chapter 3 is basically what I do. There's a bit of a nudge here and there, but otherwise my process of telling a story doesn't feel quite so much as making something up as discovering it.
I use WordPerfect, and I always compose double-spaced in Courier 12 point font. I'm old enough that I've been using WordPerfect since there was an actual competition for the office space between WordPerfect and Word, so to a degree it's a legacy application. That said, it does something no other word processor I've used does, outside of Notepad - using it feels like using a typewriter (so, to start a chapter, I hit the keys to centre the line, type the title, hit return, and the cursor is back on the left and I can just start typing). It's great - all I have to concentrate on is the words, and nothing else. As for the font thing, I can't really explain it. If I try composing in any other font, like Times New Roman or single spaced, it screws me up.
I very often will write the prologue and/or first chapter, and then the epilogue, and then I'll go back and write the other chapters in order. Not sure why I do it - it's like my brain needs an end point to work towards.
And here's Re:Apotheosis - if you read it, please do comment! There are a lot of twists and turns coming, and I'd kind of love to see how people are reacting and what they think will happen (and it will be interesting to see if they get it right...).