But in most cases, I tend to mull over the ideas I have, to do research which sometimes adds new direction - be that research in the sense of canon rewatching/rereading or research in the sense of finding out background facts -, and to let the ideas grow. Sometmes, not often, but sometimes, I talk about these ideas with other people. (This was most recently the case with one of my two Yuletide stories.) Generally I like to work on my own until I've done a first draft, but it can be both necessary and profitable to bounce ideas off someone.
Once I've pondered, let the ideas grow into somthing more, have done my research etc., I write the story. Read it through on my own. And go off in search of that most invaluable of writer's help, a beta-reader. Seriously: whether you're a newbie who has just completed her first story, or a veteran of decades, beta readers always help. (I don't always have them, granted, but that's more an availability and fandom knowledge question.) In the case of my fanfiction, there's an additionional reason, to wit, English isn't my native language, and while I'm reasonably fluent I still make mistakes now and then, especially in the written form.
I have the rough outline of a story in my head before I start to write them - i.e. I know what will happen to the main characters, where I want to go with them. Something I've never experienced was to start writing with no idea of how a story would end. Otoh it does happen that supporting characters (supporting in my story, not nessarily in their original canon) suprise, in the sense that I had no specific ideas about them in mind when starting to write beyond some vague awareness they would show up, and then they suddenly get a key scene or two, if it's a longer story.
Writers' block: also sometimes happens. In which case my usual method of dealing is to write something else, or nothing at all: I can't write half heartedly. But sometimes working on another project clears your head and emotional cluster, I've found.
Writing, technically: I type. My first few stories, as a teenager, were written by hand because I'm that old, and I switched to using computers and type my tales when I was 19-ish. Also: I need quiet. Music can be a good way to relax between writing sessions, but not during, not for me. It distracts me. And speaking of distractions: I don't care much where I'm writing, i.e. at home or in a hotel room, as long as it's quiet and I have any research material I might need to recheck available. But people and phonecalls can be serious distractions wherever I am.
December Talking Meme: the other days