I think the more efficient way would be to start reading and focusing on how to write in the first place and then focus on editing your work. This approach is going to save you a lot of time.
Perhaps the fastest way is to get some professional help which often is free in academic institutions in the form of academic writing courses. If you get the opportunity through these classes to show your writing to a linguist you can gain a lot.
If that's not an option then some classics on writing are:
- White, E. B., & Strunk, W. (1972). The elements of style. MacMillan.
- Zinsser, W. (2006). On writing well: The classic guide to writing nonfiction. Harper Perennial.
Perhaps then you should start focusing on editing and I recommend these for the start:
- Cook, C. K. (1986). Line by line: How to edit your own writing. Houghton Mifflin Harcourt.
- Ross-Larson, B. (1995). Edit yourself: A manual for everyone who works with words. WW Norton & Company
BUT personally the most important guide for me was the edits/comments that I got back from my supervisors, mentors and senior collaborators during the years. I checked their edits over and over again to systematically diagnose what was wrong with my writing and I think those edits/comments were the most helpful resource. I went as far as creating a corpora of literature relevant to my fields of research to know how exactly people write in my domains of interest in engineering and social science but well that's going a bit too far in the beginning.
Also one thing that I have noticed which makes a major impact on my editing is switching the edits on screen and on paper. I usually first do a round on screen. Then print and do it offline and then switch again! I don't know about others but in my case I tend to focus on completely different issues on when checking the scree or printed material and if I only do one I will miss a lot more.
2014 EDIT: One additional method for editing your work is listening to it. Text-to-speech software are really helpful here and you will pick up issues that you might normally neglect. There is something magical about listening to your writing which is totally different from reading it. I definitely recommend trying this as well. Obviously the betterhigher quality text-to-speech software you use withthat have more and better natural voices the betterwill enhance the experience...