My process is a bit amorphous. I write through from beginning to end with no outline but a pretty good idea of where I'm going, with the details filling themselves in as I go. If I hit a snag or realize I don't like the direction I've gone, I start a new file. Usually this just means copying and pasting over the chapters I'm okay with, then going from there. From time to time, this means starting over from the beginning. After I reach the end, I go back and edit. If it's minor edits, I won't start a new file, but if I start rearranging or cutting scenes/chapters, I start a new file. Each time I do this, I name the file TITLE (n+1). So the first file is just TITLE, the second is TITLE2, the third is TITLE3, etc. Most my WIPs are at around 10-13. Within a file, if I have paragraphs or scenes I don't need anymore, I move them to the end of the file and put them in italics. I keep copies of everything on my computer, a thumb drive, and Dropbox. After every writing session, I save in all three places. To help ensure that I'm not accidentally opening and working on an old version, I put the "last edited" date at the very end of the file. Sometimes I'll describe what I did briefly, to further help me keep track of what I've been doing. This way, I never delete anything, I have backup, and I am keeping track of my versions.
I have never edited my writing in hard copy and never will. I'm too prone to squishing and pinching and swapping and slicing-and-dicing. I can't imagine how tedious it would be to mark that down on paper, then go back to it x days later, decipher what I meant, and transfer it to the file. I'd much rather just edit right on the screen. Of course, some people love to edit on paper! Whatever works for you.