Writing is a massive part of academic life at all levels.  The more drafts you go through, the more familiar you will be with the material and the less likely you are to catch mistakes as you work.  So here is the best tip I have on the topic:

Before you consider any writing assignment “done”, read it out loud
Slowly.  Clearly.  No jumping ahead.  Every single word. 
Pause at the commas.  Stop at the periods.
Say it with inflection, as though it were a speech.  LISTEN to yourself.

Why? Reading aloud requires a different set of neurons to fire than working on your screen.  As such you will see the text differently.  You will catch things like errors in tense, missing words and inconsistencies in pluralizations.

Personally, my dogs are getting a PhD right along with me.  I read my work to them.  I stop every time I find something awkward and reword it or figure out what is wrong.  I read it slowly, word by word.  I put inflection into it as though I were delivering it at a conference.

Case in point;  I thought I was done with my 2 page research proposal until I started reading it aloud.  All of a sudden I found myself wondering if a particular sentence should be have/has, clarifying my language, shortening sentences and fixing all sorts of little stuff.  I made more than a dozen changes in 2 pages during my read through.  I’ve made 3 so far on my read through of this post.

Of course getting someone ELSE to read your stuff is always good as well.  They can catch style issues.  (For example, in case you haven’t noticed, I’m wordy )  But reading it aloud will let you catch a lot of things first and allow your editor to focus on more substantive comments about your logic or your writing style.