On attitude to academic writing
I like Write to the Top by Johnson. It has 65 short gems on how to structure an academic writing life; most of the tips are applicable to graduate students.
On Writing Well by Zinsser is a classic. It's not a recipe kind of book, but closer to something like those "Chicken Soup" series for writers. When I felt not very productive I read this as a "cleansing."
Academic writing pitfalls
A must have is Booth's the Craft of Research. It talks about the whole process of research from generating arguments and hypotheses to writing up the thesis or paper.
I also like A Manual for Writers of Research Papers, Theses, and Dissertations by Turabian. It's more of a style book, very clearly laid out and approachable.
Smart ways to structure the process
This is really "my grandma's potato salad is the best" kind of answer. No one can tell you because they probably will tell you different things that work for them. Here are what I use and have found useful. (If that helps, I work in biomedical field.)
I use Evernote to organize writing projects. I also incorporate Zotero or other bibliography software like Endnote (I like how Endnote allows me to link to PDF and comment them). I have also recently started using Docear to manage the thought process and it was fun. I also like Scrivener although I prefer physical note cards and Evernote. The key is to keep all resources in one place that is very accessible. Keep backups of your work.
For the writing process, setting up a ritual is important. Silvia's How to Write a Lot would be a nice inspiration. Pretty much the key point is: write every day for a fixed amount of time at a comfortable place. One hour, two hours, it does not matter, what matters is that you write.
Ways to make my writing more readable and make it flow better
Two eye-opening titles for me are Williams's Style: Toward Clarity and Grace and Schimel's Writing Science: How to Write Papers That Get Cited and Proposals That Get Funded.
Style: Toward Clarity and Grace is just simply wonderful. Starting from just "Subject + Verb," the book builds a framework on how to structure a statement based on one main theme: to be clear.
Writing Science dives further to analyze different levels from word use, syntax, sentence, paragraph, to the whole article using components seen in storytelling (Opening, Challenges, Action, Resolution) and their variation. It even discusses how different words in a sentence form a relational "arcs" and how to place and pace these relations for best clarity.
A classic that I must also mention is The Elements of Style by Strunk and White. Also having an easy access to Chicago Manual of Style, APA Manual (I use AMA), and Gregg Reference Manual on your desk would be tremendously helpful when any stylistic questions arise.
If you'd be writing about statistics, I'd also recommend Miller's The Chicago Guide to Writing about Multivariate Analysis which covers basics on par with writing statistics for news. For more advanced writing examples, Huck's Reading Statistics and Research is a good option. It talks about how to read results of different statistical techniques with plenty of examples from journal articles.
Freebie that you didn't ask but I want to tell anyway:
Break in by practicing free writing. It helps me focus in the morning before my writing hour.
Meet with an editor or academic writing coach who is familiar with your field for an assessment. Show your work and get a general sense of areas to improve on.
Just write. It's not possible to become a good writer by reading about writing. Remember: to suck at something is a start of being excellent at it.