How to write clearly

Someone reading your essay won't have you there to explain to them what is going on. For this reason, the burden rests on your shoulders to explain yourself in such a way that you cannot be misunderstood.

Words

Always explain jargon: imagine your reader is intelligent but does not know the subject, so that you have to explain theoretical concepts. Further, don't use more jargon than you have to, and more generally, don't use a complicated word if a simple one will do.

Use terms consistently. Some students try to avoid repetition by changing terms for what they see as synonyms. Don't do this. In philosophy, a change of term normally signals a change in subject. If it feels like you're repeating yourself, then you need to think about the structure of your essay, and not simply try to mask repetition by changing terminology.

It's ok to use the word "I", in some circumstances. For example, your essay might begin "In this paper, I will show that...". This use of "I" is perfectly acceptable, and certainly preferable to the hideous "In this paper, it is shown that…". But conversely, only use "I" when it is necessary. Do not autobiographically write: "For me, X is false. I feel this because...". Instead, write: "X is false. It is false because...".

Sentences

Shorter sentences are almost always better sentences. If you can cut a sentence into smaller chunks, do so. Look at your sentences and think about how they might be shorter: try to find ways to express your claims more concisely. Doing so will allow your essay to cover more ground, and also make it easier to read.

Paragraphs and structure

Each paragraph should make a single and self-contained point. If a paragraph is longer than a few lines, you almost certainly need to break it up. Make sure that your paragraphs follow on from one another in a way that is transparently systematic. This is easier if you signpost to the reader what's going on. Use phrases like "So far, I have shown that...", "I will now show that...", and "One might object to the previous argument by... But this is mistaken because...".

Referencing

Failing to reference properly will land you in serious trouble. There are many ways to reference, but the Harvard system is relatively standard in philosophy. Insert "(Surname Year: Page)" in the text, and then include an alphabetical bibliography at the end containing more complete details of the sources you cited in the main text. Look up how to format these. Sometimes it is quicker to find someone else citing the work in question and copy+paste their reference. If you are beyond undergraduate level (e.g. you're a PhD student), I'd advise using Zotero to help you with referencing: it's easy to learn and makes things much faster in the long run.

Some simple but common mistakes

This list is inevitably arbitrary: the more general rule is to always look things up if you aren't sure. Make use of your teachers and/or google.

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Larry Trask has an excellent and comprehensive guide to punctuation here.