Garner's books are great; Elements of Legal Style is a good starting point. Your goal as an associate should be to produce writing that is free of stylistic mistakes (and also grammar errors and typos, of course). That sounds like a low bar, but it will put you ahead of most of your peers. Passive voice is the most common stylistic mistake. Learn to recognize it and to eradicate it. Other common stylistic mistakes at the sentence level include lack of parallel construction, poor word choices (e.g., "prior to" instead of "before"), and sentences that are longer than necessary. Learn to recognize and correct all of these.
From a structural level, learn to outline before you write. And if it is useful to you, learn to use the "madman" method that Garner describes in Legal Writing in Plain English and elsewhere. Also, train yourself to always use roadmap paragraphs and short topic sentences for each paragraph. If you can consistently produce writing that follows all of these rules, you will be in very good shape. They are simple but too often ignored.
Here are a few other tips that are simple but improve readability by miles:
Always do your very best to avoid acronyms. Do this by introducing the best short forms you can think of. If the partner disagrees, then she can switch back to acronyms. Acronyms are most often a crutch, but sometimes they are common in a given practice area even though unfamiliar to you. What I'm saying is make sure you don't use them as a crutch. And certainly don't introduce any new ones. Footnote one here is a good example of the problem and a remedy:
https://www.cadc.uscourts.gov/internet/ ... 869487.pdf.
Use relative time spans rather than precise dates (unless the precise date matters). So if you are writing something like a chronology you would begin with "In November of last year" or similar, and then the following sentences would say "One month later..." "Several months later..." "Around the same time..." etc. If you must use a series of precise dates, put the dates at the end of the sentence. Likewise, put long citations near the end of paragraphs where possible. Also, use pronouns or names instead of designations ("Smith" is better than "Defendant").
You may be thinking: "This is all too basic; I want to learn how to write really well--not just follow simple rules." As basic as it sounds, good lawyers flout these rules every day. Part of it is that they don't care. Part of it is that they're too busy to do a better job. But the more you internalize the rules, the better you'll be at implementing them in your first drafts rather than your second or third.
Following these and the rest of Garner's rules will guarantee that you produce clean, intelligible drafts that most lawyers will recognize as good writing. Of course, your ideas must be good as well, but that is another matter. The next step is to layer your writing with the rhetorical devices that elevate great writing over the merely good: analogy, metaphor, alliteration, turns of phrase, captivating intros, etc. Garner's books won't teach you how to do that. I don't think anything can teach you how to do that, although some have made efforts to:
http://www.wardfarnsworth.com/. You won't be expected to add any of these "bonus features" to anything you write (although if you do, and do it well, people will appreciate it).
In short, learn and follow Garner's rules.