To write well, you need to spellcheck and grammarcheck your work. But you need to do more than that. Someone reading your essay won't have you there to explain to them what is going on. The essay has to stand on its own. The burden rests on your shoulders to explain yourself in such a way that you cannot be misunderstood.
More specifically, you need to use the right words, write readable sentences, make good use of paragraphs, and structure what you write in a transparent way. Towards the bottom of the page I also briefly discuss referencing and mention some common mistakes.
Words
Define the jargon at the start. 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 always signals a change in subject. If it feels like you’re repeating yourself, then you need to think about the structure of your essay, not try to cover it over with new words.
Avoid informal terms such as "rubbish" and "silly".
Avoid weasel words such as "surely" and "basically", which are all too often used instead of good arguments and correct summaries.
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 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.
Make sure that your sentences are direct and concise. Don't write: "I shall now endeavour to investigate the nature of the ontological argument and evaluate whether or not we should find it compelling." Instead write: "I shall now describe and evaluate the ontological argument."
All questions, and only questions, should end with a question mark. At any rate, asking questions when you’re supposed to be answering a question is usually a bad idea. Replace rhetorical questions with statements, and don’t ask any question that you don’t yourself explicitly answer.
Paragraphs and structure
Each paragraph should make a single and self-contained point.
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...".
Split your work into sentences around fifteen words long and paragraphs around six sentences long. (Most word processors can display your average sentence and paragraph length.)
"Therefore" and "so" mean "what follows this term is justified by the previous sentence or paragraph". If it doesn't follow, don't use the term. If it does follow but it's not immediately obvious how, elaborate on the connection.
Referencing:
Failing to reference properly will land you in serious trouble. There are many ways to reference: check your handbook. Here’s how I usually do it: I insert "(Surname Year: Page)" in the text, and then include an alphabetical bibliography with "Surname, Initial. Title. Publisher (Year)", for everyone I reference. So you might have “Mackie writes that ‘The sort of God required for Pascal’s [argument] is modelled on a monarch both stupid enough and vain enough to be pleased with self-interested flattery’ (Mackie 1982: 203)” and then “Mackie, J. The Miracle of Theism. Oxford (1982)” in the bibliography.
Some simple but common mistakes:
"Refute" does not mean "deny". It means "conclusively disprove".
"Begs the question" does not mean "raises the question". It means "assumes what it sets out to prove".
"e.g." means "for example". It is not interchangeable with "i.e."
"i.e." means "that is". It is not interchangeable with "e.g."
"Logical" does not mean "sensible" or "calculated". It has a very specific meaning in philosophy. If you don’t know what that meaning is, don't use the term.
"Infer" does not mean the same as "imply". You might imply something with your words, and I might infer something from them. Never the reverse.
"It's" always means "it is".
Saying that X is relative doesn't say much unless you know what X is relative to. So tell us what, and why.
The word “subjective” is ambiguous. If you use this term, you need to explain what you mean by it.
Claims, propositions, positions, theories and views can be true or false. It's very confusing if you refer to them as valid, invalid, sound or unsound.
Arguments can be valid, invalid, sound or unsound. It's very confusing if you refer to them as true or false.
Since positions and arguments do not have minds, they cannot "believe" anything. They can only state, imply, entail, and so on.
Semi-colons can only be used in very particular and extremely rare circumstances. Unless you are extremely confident that you know what they are for, don't use them.