Without a computer, the mechanics of writing would be too tedious for words. Of course I write on a computer. I print a hard-copy of every draft. The number of drafts run anywhere from a minimum of three to a maximum of ten.
I correct on paper as well as on-screen as I'm writing. I do not, however, proofread my own stuff. I'm too familiar with it and it's just too easy to skim over stupid--and I mean REALLY stupid--mistakes.