"How to write" books are often an awful mess of superstitious prescriptivism. To be fair, the people reading your essays may have also read these books, and in this case it's good to know that they may look down on you for splitting infinitives, ending sentences with prepositions, and using various other perfectly fine English constructions that someone a hundred years ago decided were ungrammatical because they don't work in Latin. (See Language Log for some informative rants on this subject.) There's good stuff out there, but don't count on finding it easily.

If you want to learn to write well, (1) read a lot of fiction by successful authors (good writing style affects success more there than it does in, e.g., the sciences) and (2) write a lot, preferably in a forum where your writing will be read and criticized frequently.

In particular, the fiction of Isaac Asimov has done a lot to improve my writing. His writing (both fiction and nonfiction) is perfectly clear and transparent, to the point that you don't even notice there is a style. Even if this isn't the kind of writing you're really interested in, I think everyone should have this style in their repertoire.