Commenting on a first draft:
Strunk and White's favorite aphorism is, "Omit needless words". Observe that "Omit needless words" is an example of itself: it could hardly be written more compactly. As with any rule, one could go overboard with this aphorism, cutting and cutting until the whole purpose of writing is lost. Nonetheless, experience suggests that bad writing can often be improved by cutting. What is more, reducing the word count will frequently clarify other problems: when you use fewer words, you are compelled to choose your words more accurately, and this will require you to decide what you really wanted to say.
Think of words as money. When you write a 1000-word essay, you want to get your money's worth. It would be a shame to provide the reader with only 800 words worth of content, or only 500 words worth. Yet this happens all the time. The problem, often, is that the author assumes that words are free. If a sentence seems unclear, the author will add extra words until it starts to approximate the intended meaning. In the process, however, the ratio of meaning to word-count is actually going down. It's much better to express the idea accurately in the first place, and this will only be possible once the extraneous words are cut away.
Some words can simply be cut without any further changes. Ask yourself: "if I simply omitted this word, would the meaning remain effectively the same?". Most adverbs fall in this category. The words "essentially", "basically", "very", and "really" are usually superfluous. Authors use these words because they seem to intensify the meaning. And they do. But they also take up space, so that their net effect is negative. Which is the better sentence, "John ran very fast" or "John ran fast" -- or, indeed, if we drop the adjective as well, "John ran"? Complicated sentences are not bad, but needlessly complicated sentences are.
The first assignment, then, is to draw red lines through all of the words that can be deleted from the author's draft without changing its meaning.
Now let's move to the sentence level. Grammatically complicated sentences can usually be simplified, and the monetary metaphor helps explain why the simpler sentences are often better. A complicated sentence such as "The key went into the lock where it was put by John" has a low ratio of meaning to words. Most of the words ("the", "the", "where", "it", "was", "by", and perhaps "into") are simply functional words that hold the sentence together without providing much information. And two of the words ("went" and "put") provide effectively the same information: they report that the same event took place. Which words do convey information? "Key", "lock", and "John", to be sure, and then one or another of the words that describe the action. Having identified which words are necessary to express the thought, we can construct a straightforward sentence: "John put the key into the lock". This sentence still includes some function words ("the", "the", and maybe "into"), but many fewer than before.
The second assignment, therefore, is to go through the author's draft with a green pen and underline all of the words that provide information that the reader needs to comprehend the essay. These will typically be nouns and verbs. If the same information is provided redundantly by two or more words, either in the same sentence or in adjacent sentences, then draw a line to connect them. Then identify a few sentences, if any exist, that contain large numbers of words that convey no information. Rewrite those sentences more simply.
Next, let us consider sentences as a whole. Does the author's draft include two or more sentences that express a similar or overlapping idea, perhaps in different words? The similarity may not be obvious, and you may even feel an emotional attachment to both formulations. The redundant sentences may be located in the same paragraph, or in different paragraphs. Sentences can also be redundant because they don't say anything. For example, first drafts frequently commence with a couple of sentences (or even a couple of pages, of throat-clearing platitudes such as "Computers are having a powerful impact on the world in which we live", and such sentences can simply be deleted. The third assignment is to cross out all of the redundant sentences in the author's draft.
Finally, let us consider the bottom line. Having assessed the author's draft essay on several levels, how many words worth of meaning does it contain? For the price of 1000 words, has the author bought 1000 words worth of meaning? Or, if someone put a gun to your head, could you cut the essay to 800 words, or 500 words, or even 300 words, without cutting anything important? Provide the author with your estimate of the smallest number of words that could be used to provide the same information.