Nomad Scholar writes well at Inside Higher Ed on the surprising process of writing--an essay spurred by Shari Wilson's realization that certain of her students write better on in-class exam assignments than when they write essays at home on their computers. And she also links to a really fascinating essay by Daniel Chandler on "The Phenomenology of Writing by Hand."
I find these questions about process endlessly interesting. I want to teach a writing class again one of these days and delve back into issues in the classroom that I more usually now tackle one-on-one when I read manuscripts for students and colleagues and friends and so forth. (I've just finished reading Samuel R. Delany's book on writing, about which more shortly.)
I write almost everything by hand. I find it invaluable for keeping the sense of momentum, of something having a shape and forward movement as well as local interest. The two kinds of writing I do directly onto the computer, exceptions to this general rule, are lectures (i.e. what I write to deliver for my lecture classes, where I type notes up from the book I'm teaching and then fill in what I'm going to say around it) and blogging. Occasionally I write an academic talk in "lecture" mode--i.e. directly onto the computer (I did it for that Boswell-Johnson thing last week, since it was for a more general audience rather than strictly academic)--but it's rare.
More usually my academic writing proceeds through stages: read books and stick them full of post-its; type up those notes onto the computer; mark up all of my notes on primary and secondary sources with what's important, coding it into a messy one-page handwritten outline with a rather disorganized numbering system (maybe there are 20 different primary sources and 40 critical ones and the coding ends up all, like, 5.1 Insert Williams2); build an armature (that's the word I always think of, and I visualize it as something like the chicken-wire frame you'd build if you were going to make a massive papier-mache animal, a bull or a lion--you have to get that frame right so that as you do the fun part afterwards i.e. slap on the stuff & shape it how it is meant to be and later paint it and do general finishing it all works right) of quotations and footnotes (in an aside, I will say that I've seen the "my weird habits" meme around the place and thought--no doubt completely erroneously--"Oh, I don't think I can do that one, I may have weird habits but by definition they do not seem weird to myself so I do not really think I have any"--but perhaps it is one of my stranger habits that my footnotes are always perfect before I even start writing, all the bibliographic information and stuff is all filled in & in the right format and everything--I love footnotes, I find all that stuff enjoyable, but it's also a question of getting all the ducks in a row so that I can really have fun and write the first full draft fast). That's all been done on the computer; then I sit down with that very full outline/quotations thing all neatly printed out (maybe it's 30 single-spaced pages if it's for a book chapter) and write the chapter from start to finish with pen and paper, again marking inserts of the "3.1 to p. 7 draft" variety. Then I type it up (hard work because it's a mess), fixing up as I go along. Then I edit. Edit again. And again. And many times more. (Each stage also brings to light a few things I still need to go and read and sort out, but by late on in the process the library work required is only the odd "check this quotation" or whatever.) I find academic writing deeply enjoyable, it is exploratory and interesting but on the whole not very stressful because it comes so clear to me as I'm reading what I feel I will need to say about the things.
Writing fiction is much harder, because it involves letting yourself go & see where things take you; less planning, more discovery, in the terms of that "writing by hand" essay above (though really both kinds of writing involve lots of discovery and a certain amount of planning, if they didn't have the former they wouldn't be interesting to do & if they didn't have the latter they wouldn't be interesting to read). I write my drafts with pens--usually those really excellent Japanese gelly roll pens, which lay down a satisfyingly slug-like trail of gleaming ink--in little books, little so that your 1500 words or whatever the daily amount is covers 4 or 5 pages and makes you feel productive. Then type up a big swath of pages (maybe wait till it's a third of the way written, type up a bunch all at once), then lots more printing and editing. I have not yet written a novel that didn't involve the other kind of draft-writing, the "oh, six months later I can see it now needs another drastic edit"; "oh, it's six months later again and now I can still see how to make the book better"; etc. Which is one of the things that makes me amazed by but also slightly skeptical about the book-a-year writers, let alone by the multi-book-a-year ones. But this may just be a matter of individual difference.
When I was a young person I had a stage of a few years where I could only compose literary stuff on the typewriter or computer. Also (like reader of depressing books, who has what is surely one of the most distinctive voices of all the bloggers I read) I could only use lower-case letters, and in particular I was almost physically incapable of using an upper-case i. So I wrote a lot of poems and stories all in lower-case and then a few years later on I was not so depressed and grew out of the habit but there is no doubt that when you are feeling a certain way it is almost impossible to stake your place on the page with a capital I. (I also had a long time of really wrestling with the conventional use of quotation marks for speech, I was reading a lot of experimental stuff and it really seemed too deadening to have those ridiculous "" things all over the place, dashes seemed infinitely preferable. But at some point I realized that as a reader, I found most writers' attempts to invent new systems for handling this distracting rather than effective. There are exceptions, of course, but I basically just realized I had to accommodate myself to it & it wouldn't kill me after all.)