The term "style" is often taken loosely to comprehend not only style in the narrow sense but also the larger issues of structure and form. These latter represent the "macro" aspects of writing -- the overall organization of a text and the logic with which the pieces are integrated into a coherent whole. By contrast, style in the narrow sense has to do with the "micro" aspects of writing. It deals, if you will, not with overall organization (structure) or with the way sections and paragraphs fit together (form) but with the ways words are tied together to build sentences and paragraphs. I will be concerned here with this narrower conception of style.
Writing in a clear and lively style is ultimately a skill; it is a feat of what the philosopher Michael Polanyi called tacit knowledge. For that reason, one can't learn to be a good writer by following some list of explicit rules. As in any skill, one learns writing only by practice and by imitating accomplished writers. Here is one of my favorite pieces of writing in economics.
Edit. Edit. Edit.
There is in writing a law of conservation of effort. The total effort summed between writer and reader is constant. That means that the less effort you put into a paper, the more effort the reader has to put into it. Presumably such is not the incentive you want to generate. Writing that seems effortless is actually the product of unstinting self-editing. (I put aside here the question of whether deliberate obfuscation can sometimes be a clever rhetorical strategy. Perhaps German philosophy would have been far less popular -- and the world consequently far better off -- if it had been written clearly. Hegel would have become a five-page pamphlet.)
One element of grammar is "voice." An example of the active voice would be "the man bit the dog." In the passive voice that would be "the dog was bitten by the man" or just "the dog was bitten." One often hears it said (including, in the past, by me) that one should always try to avoid the passive voice. As these examples suggest, the passive voice can be leaden, lazy, and evasive. It is often a way of avoiding thinking about what you really mean to say. (Who really bit the dog? I'm too lazy to think about that. Let's just fudge it and say the dog "was bitten.") In the end, of course, the passive voice is perfectly grammatical and a valuable tool in many cases. The real culprit isn't the passive voice: it's passive (or inactive) writing.
Cohesion and flow.
One of the marks of good writing is a smooth flow between sentences and the overall cohesion of the paragraph. And it is here that the passive is valuable. As Joseph Williams puts it, we "feel one sentence is cohesive with the next when we see at the beginning of a second sentence information that appeared toward the end of the previous one. That's what creates the experience of 'flow.' And in fact, that's the main reason we have the passive in the language in the first place: to arrange sentences so that they flow from one to the next." For a more thorough discussion of flow and cohesion, consult the resources here.
Read your writing out loud.
The best test of your writing style is to read what you've written -- out loud if necessary. Be sure to read it as written, pausing where your punctuation really demands and adding inflection the way the text actually requires. Is the text choppy and hard to read? Is it monotonous -- with all the sentences equal in length? Cadence is important. Try for a mix in which short, clean sentences punctuate long, elegant ones.
Lifeless, bureaucratic turns of phrase are not limited to expressions using the passive voice (expressions like "it should be noted that..."). One ubiquitous offender in scholarly (especially student) writing is the verb to state, as in "Adam Smith stated that..." The rule here is the same: don't use it. Almost any synonym -- "suggested," "wrote," "argued," "opined," or just plain "said" -- is better. (The only time I use the verb to state is when I'm trying to set a mock-serious tone.)
The first person.
Many people use the passive voice out of a fear of using the first person singular. The fear is unjustified. If you can't phrase something in a way that is both lively and impersonal, then go ahead and say "I." Similarly, you should use "we" if you have a co-author or if you are speaking for a well-defined group.
In mathematical writing, one often finds what I call "the engineering 'we.'" "First we divide by x and then we integrate over the real numbers," etc. This can be construed as referring to the author and the reader, who are jointly performing the mathematical operations. But many writers treat it more like the physician's "bedside 'we'" ("How are 'we' feeling today"?); and others use it as a rhetorical crutch and thought-substitute. In either case, too much of the mathematician's "we" leads to insipid prose.
English is in part a Germanic language. But one area in which English does not follow German is the use of extended adjectival constructions before the noun. This is sometimes called "telegram style," and it is a practice particularly prevalent in writing about economics. To a limited extent, stacking adjectives before the noun is unavoidable -- and even adds a little punch to one's style. But it's one thing to talk of "firm-size variables" or "sales-growth projections" and quite another thing to describe "prior period sales changes" or "the total net long-term portfolio capital flow." It may take slightly more space to say "sales changes in the prior period" or "the total net flow of long-term portfolio capital"; but it definitely scores lower on the bureaucratic-prose index. Stacking can also confuse or change meaning, sometimes inadvertently. Is a foreign-exchange student an exchange student from overseas or someone who studies foreign exchange? The rule I use for hyphenation is this: when two or more nouns are used as adjectives modifying a third, absence of hyphens indicates that all the adjectives modify the same noun.
News reporters have the job of conveying a lot of information in a small amount of space. Thus, they often cram together several unconnected pieces of information in the same sentence. "An unemployed electrician from Florida who likes tapioca pudding for dessert, Hawkins, 36, admitted at his trial, which entered its 257th day yesterday, that he strangled his estranged wife in Hawaii, which was the 50th state to join the Union...." You're not a newspaper reporter. Stick to one thought per sentence.
It is a mistake to think that elegant writing means avoiding all contractions (saying "cannot" instead of "can't," for instance). In modern American style there is no such rule. The best advice is to mix contractions and non-contracted forms, and to avoid a pedantic sound on the one hand and an excessively breezy sound on the other.