Here are some tips that will help you avoid common mistakes, write better papers, and give more compelling arguments for your position. They are especially relevant for courses in analytic philosophy, but a lot of these tips are general purpose. The point is simple: to help you think (and express yourself) more clearly and concisely. Without any further ado, then –

Get to the point. At the start of your essay, don't say, ‘For thousands of years, philosophers have been stroking their chins and furrowing their brows, wondering about the relationship between subjective experience and knowledge about the external world’ or anything along those lines. Just get right into the argument. So, ‘In the Meditations, Descartes argues X. His main support for this view is Y. I am going to argue that Y leads to a dilemma between views A and B. I will show that B is unappealing for three main reasons and suggest, therefore, that we should accept A instead. I will consider two main objections to A but show that these can be overcome. Ultimately, I conclude Z.’

As you develop as a writer you can sometimes move away from this blatant way of setting things up without detracting from clarity. But you can almost never go wrong with an introduction like this. For course assignments, at least, you should favour simple, straightforward, clear writing, where you ‘put your cards on the table’ and make things as obvious to the reader as possible. One way to do this is to. . .

Front-load the paper. Specifically, by the end of the first paragraph or two (depending on the length of the paper, perhaps the first page), the reader should already have a ‘map’ in their head of what is going to be covered in the essay and enough specificity that they have a fairly good idea of the basic content and structure of what you are going to argue. This way, as they read through the rest of the essay, they can more easily follow what you're doing (as you fill in the various details of the argument) because they have the basic idea in mind already.

Some further tips:

Use short, simple sentences. You should typically use shorter sentences that each are ‘doing’ one thing or conveying one logical move. Long, complicated sentences with lots of interlocking, embedded clauses should usually be avoided.

Connect the dots. Imagine that you are trying to explain your argument to a smart twelve-year-old. Now imagine that it is very, very important that they understand your argument, or a bomb will go off, killing everyone in sight. You don't want to skip any steps. You don't want to assume they'll see the connection between two points. You don't want to say anything more than what you need to convey the precise point you are making. You don't want to use a fancy word where a simple word will do. You don't want to refer to the same thing with three different words so that they aren't quite sure whether you're talking about one thing or three things, and so on. To get into the right mindset, it might be helpful to . . .

Think like a computer programmer. Imagine you are a computer programmer. Instead of writing a philosophy paper to convey your argument, you are writing lines of computer code. Again, if the computer program doesn't run properly, a bomb will go off and everyone will die. There is no room for ambiguity. If even one character in one line of code is wrong, the code will break (and everyone will die).

This has several implications:

Use consistent variables and definitions. Once you define a term or variable to mean a specific thing, you should keep using that same term to mean that exact same thing throughout the rest of the argument. If you define ‘free will’ to mean ‘having the ability to make choices that cannot be fully explained by any prior cause either internal or external to the agent’ then you must continue to use the term ‘free will’ (not some random new term like ‘free choice’ or ‘free decision’) to mean exactly what you defined that term to mean. If you define a variable, X, in a computer, and then you suddenly start using the term Y to refer to whatever X was defined as, the code will break (and everyone dies). If you use X to mean something even slightly different from what you defined it as, the code will break (and everyone dies).

Use precise definitions. You should define terms very precisely, ‘building into’ their meaning exactly what you need for your argument to work and nothing more. Don't define ‘free will’ in the way suggested above if your argument only requires that choices not be fully explainable by prior causes that are external to the agent (but internal causes are okay). Another point: unless it is completely clear and unambiguous, you may also need to define terms within definitions of other terms, especially if the meaning of the first term rests in an important way on how the second term is understood.

Qualify your claims. Qualifying statements and words that constrain the scope of a claim (like some, most, every, many, always, never, often, sometimes) can be really important. Be specific. Instead of saying ‘People learn from their mistakes’, say, ‘People usually learn from their mistakes’, or ‘People sometimes learn from their mistakes’, or ‘People learn from their mistakes often enough that . . .’ or whatever you specifically mean. Also be very careful about using terms like ‘always’ or ‘never’ or ‘every’ that admit of no exceptions. If you rest your argument on a claim like this that admits of no exceptions, all someone has to do is come up with one counterexample and they defeat your whole argument. Don't leave yourself open to such refutation. If you say ‘always X’ you had better be sure that there are not exceptions, and that a softer, more qualified claim won't work to make your argument go through.

Remove ambiguity. Clarify ‘indexical’ terms (like ‘this’ or ‘that’). For example, when you say ‘This’ in a new sentence, referring back to something in the previous sentence or paragraph – unless it is blatantly clear what ‘This’ is referring to – you should usually add a word or phrase after ‘This’ that disambiguates what chunk of the previous sentence or paragraph you are talking about. So, less good would be, ‘Much has been written about the Funky Banana view and there are arguments in favour of its main premise as well as against it. This is worth exploring further.’ Better would be, ‘Much has been written about the Funky Banana view and there are arguments in favour of its main premise as well as against it. This disagreement is worth exploring further.’

Two more random tips:

Steel your opponent's view. Try to give a ‘steel’ rather than ‘straw’ version of the view you are critiquing. If you are going to argue that someone's argument fails, don't give an uncharitable, sloppy, obviously implausible version of their argument and then knock this ‘straw’ version of it down. Instead, present their argument in the most charitable, precise, plausible way you can, and show that, even in this ‘steel’ form, it still doesn't work.

Show us the argument, don't tell us what to think or what you feel. Generally avoid saying ‘I believe X’ or ‘I feel that Y’ or ‘In my personal opinion, Z.’ In philosophy, the reader is not usually interested in what you personally think or believe or feel about some topic. Instead, they want to know what your arguments are, so that they can see for themselves whether those arguments work and make up their own mind about what to think on the basis of them.

Be humble. Don't say stuff like, ‘As I will prove’, or ‘As is completely obvious’, etc. First, unless you are literally proving a mathematical theorem or completing a proof in logic, you probably won't prove your claim. At best, you will provide strong arguments in favour of your view; but these arguments can almost always be challenged on some legitimate grounds or another. And second, although some things may very well be completely obvious (in which case you don't need to say so), a more common situation in philosophy is that something seems really obvious (like, that tables exist), but when you really think about it, you start to realize that things may not be so obvious after all (maybe all that truly exists are atoms arranged table-wise).

Finally:

Less is more. Pick a smaller, more narrow thesis or topic (hopefully one that is still interesting or matters in some way!) and argue for it thoroughly, rather than a more ambitious thesis or topic for which you argue less thoroughly. If you think you have finally settled on a sufficiently manageable thesis, it is probably still too big. Really giving a strong argument where you fully consider the most plausible competing views and compellingly rule them out is hard. The bigger the topic or thesis, the less well you will be able to pull this off in a short paper.

And now for a clarification:

Strong claims. In philosophy when someone says you've made a ‘strong claim’, this does not usually mean you made a good or convincing claim. It usually means you made a bold or big claim, which means it will require a lot of support for the reader to believe it. So when someone says, ‘That is a strong claim’, they are often trying to convey something like, ‘That is a claim that is very ambitious – perhaps too ambitious. Can you really support such a bold claim?’ Likewise, a ‘weak claim’ is not usually a bad or unconvincing claim; it is more like a ‘softer’ or easier-to-defend claim. Now, sometimes you do want to make a strong claim, when you really have the resources to defend it. If so, go for it. At other times, a weak claim is all you need to make your argument work, and in that case, it is often better to go with that weaker claim (since it is easier to defend).

This is just a toolkit to get you started. Almost all of these rules can be broken, to good effect, by sufficiently sophisticated writers. But see if you can get these basics down first. It will probably serve you well in the long run.