The hardest step for me in writing papers was selecting a topic. It had to be interesting enough to hold my attention for the duration of the writing, narrow enough in scope to be manageable, a topic where I felt there was some worthwhile point to be made or conclusion to be drawn, and of course, had to fit the requirements of the course. The narrower those were, the easier to find a topic. I would often spend perhaps a quarter of the entire time I had on this step, because if I didn't make a good choice, the whole process went downhill from there and I could easily be left starting from scratch with only a quarter of the time left.
Once I had a general topic, I did my background reading and research, to collect all the details necessary. It was during this step that I refined the exact approach I would take in my paper: what was the point I was trying make, the conclusions I wanted to draw, the thesis statement I wanted to support? A general outline would start to form out of the gathered information almost unbidden. I would then start to steer the research more pointedly, to fill in any gaps and answer remaining questions.
In terms of mechanics, for short or highly focused papers (e.g. literary analysis of a specific story), I took my notes on paper and that was easy enough to work with when the actual writing part came. Even for longer papers, though, like my undergraduate thesis, I could never get into the notecard method. I still took notes on papers, using underlining, highlighters, and marginal notes to categorize information for easy retrieval. Only rarely did I ever take notes directly on the computer. (Now, though, in the technical papers and reports I write, my "notes" are already on the computer, in the form of experimental data, and papers - usually brief - in electronic format.)
The most important part of the writing process for me has always been making a good outline. I make this in my actual document, so when it is complete, I can just go back and flesh it out with sentences and paragraphs. The outline is driven by the structure of my ideas, not pages or paragraphs. I start with the introduction, and include in it all the points I want to make there. Then I go section by section, again listing broadly which points go where, and in which order. Finally I outline the conclusions, which for me is never simply a restatement of the introduction or top level summary. Yes, I do go back to the main point stated in the intro and sum up the final conclusions, but usually also go beyond this somehow, perhaps elaborating on its importance, or questions necessarily left unanswered.
I cannot overemphasize the importance of this outline step. Even when writing essay questions on exams, I found outlining to be time well spent. In fact, I almost cannot start writing until the outline is completely finished. I cannot begin until I can see my way clear to the end. Otherwise, I can end up going around in circles and never get where I want to go. Once this is clear, I can start writing, and the writing itself comes out in nearly final form. Then I deal with any mechanics like references, bibliography, etc. Finally I revisit the text for a final spelling and grammar check, at which point I may change a few words here or there, or add an example I overlooked on first writing, but I am essentially done.
I suppose I should add that this method has always produced good results, both in terms of grades, and my personal satisfaction with the work.