Learning to write mathematics properly is much like learning to write any language properly, only more so because such a premium is placed on logical organization and clarity.
Mathematics, both the part that is written in words and the part that is written in symbols, is attempting to convey meaning. When you write and read symbols, think about what they say when you read them out loud. Every time you see the symbol $=$, remember that the symbol has a pronunciation when you read it, and it says "is equal to". So if you write things like
$$2x = 4 = \frac{4}{2}=2,$$
(which I see far too often on exams) then you are saying "twice $x$ is equal to four, which is equal to four halves, which is equal to $2$", which of course is false and liable to cost you points, even though you probably don't actually think that $4$ and $\frac{4}{2}$ are equal. Remember, first and foremost, that every symbol has a meaning and a pronunciation. Unless you recognize that, you won't be able to get very far.
So first you need to be clear on what you want to say, and then make sure that what you wrote actually conveys that meaning and not other meanings. If you can do that, even if it is with "plain English", you will have gotten over more than half the problem.
That said, mathematics is also a technical language with a number of conventions and jargon. The very best thing you can do to become familiar with, and good at using those conventions, is to read a lot of mathematics, with an eye towards understanding what is written and how the language helps that understanding (just like doing a lot of reading is one of the best ways to improve one's spelling).
A close second is to read books that are meant to help introduce you to proofs and logical arguments, usually with subtitles like "first course in advanced mathematics" or "introduction ot abstract/advanced mathematics". Find out what the "Intro to proofs" course is at your school, and look at the textbook they use.
One important thing is not to simply try to mimic the language you see: that will result in the mathematical equivalent of saying "Buenos días. Yo quiero estación de tren ser, por favor" when trying to ask for directions to the train station ("Good morning. I want be train station, please.") You want to keep an eye on the meaning that the words are conveying, and how that particular choice of words (and even the order of the words) matters. Notice, for instance, that saying "For every $x$ there is a $y$" is not the same thing as saying "There is a $y$ such that for every $x$...", even though they may seem very similar when thought of in English.
So: always think first about what you are trying to say and make sure you say that. Read what you've written, pronouncing every symbol to yourself to make sure you aren't saying that you "want to be train station". And read your books and professors' notes to see how the language works and become familiar with it.
Added: It seems I rather badly misinterpret the true thrust of your question (despite the fact that you seem to have "accepted" my answer). In so far as what steps to add or what steps to skip, as has been pointed out, it depends on your level. I would not object to a student in my graduate abstract algebra class going from $x(x+1)(x+2)$ directly to $x^3+3x^2+2x$ (or even not writing out the computations before using it!) but I would definitely request a precalculus student to write out how he got to that final answer. If you have to stop and think carefully about what the answer is, then you should not skip the step and write it down. For a particular class, look at the textbook and which steps it works out explicitly and which steps it skips. Look at what steps your professor works out explicitly and which steps he skips. You'll want to not stray too far from them as far as skipping more steps (though of course you can always skip fewer steps if you are unsure about a calculation/argument).
