One of the most important things a writer can do is to establish and maintain an organized record-keeping system. While this is easy for someone who produces a single finished manuscript each year (a novelist, for example), it can be difficult for a writer that produces a large number of finished manuscripts each year (a prolific short story writer or a non-fiction writer).
There are multiple parts to organizing. At the one end of the writing process is developing a method to keep track of work-in-progress and assignments with deadlines. At the other end is developing a method to keep track of work submitted, accepted, paid for, and published.
Much of my work is written on spec, so I don't often deal with conflicting deadlines. During the past few years I've probably not had more than three deadline-driven assignments overlap. It isn't hard to stick a Post-It note to my computer monitor and jot a note in my Day Planner to remind me of these deadlines. I know writers who use spreadsheets and electronic calendars to keep track of multiple assignments.
The back end of the process is where I've put most of my organizational efforts. While some writers claim to keep all their records on a computer, I find it impossible to do that. There's just too much paperwork.
Every manuscript I finish gets its own folder. Into that folder goes a hardcopy of the ms. and copies of any research material I used; a record of where the piece has been submitted and the results (rejection, request for revision, acceptance, etc.); copies of all acceptance letters, contracts, check stubs, and etc.. That folder travels around my office through various file drawers depending on what stage the ms. is at.
Under submission? One drawer for that.
Accepted? One drawer for that.
Paid for/not published? Drawer for that.
Published/not paid for? Drawer for that.
Published and paid for? Nine drawers for that.
While not a perfect system, it's served me well since I started writing more than thirty years ago. And it would be bloody hard to change now.