Perhaps this write-up leans more towards writing a good paper than getting an A, and we're certainly outside the realm of minimum effort.  That's how this node is leaning, so here we go:
  1. The quality of your argument matters.  Papers always require you to demonstrate your reasoning and critical ability, regardless of the assignment.  Watch out for logical fallacies -- comp teachers can spot an ad hominem attack or post hoc, ergo propter hoc slip from orbit.  Logic and critical thinking skills are good things to have, so if you haven't had any formal training, you might want to read around.  It's a lot of work, but well worth it.

  2. Style, spelling, and grammar matter more than you think.  No matter how good your argument is, if your presentation makes you look like a moron you will do poorly.  Papers are formal, which means that lots of liberties (like the ones I'm taking in this node with tone, word choice, parenthetical comments, and informal style) are no-nos.  If you aren't sure on a style point (like, for example, comma use in a series), decide what you're going to do and be consistent through the entire paper.  The reason you want to be so careful with these things is that teachers have to read incredible amounts of student writing.  For every paper they assign, they have to do more work than you.  Sure, it may be painful to write a ten page paper, but grading twenty five of them is much worse.  Trust me on this.  And since most of the papers they have to grade and comment on will have terrible grammar and spelling, they will be very happy when they come across a paper where they don't have to redpen every other line.  They will view that paper as a relief, and they will treat it kindly.  Sure, you'll get a better grade, but more importantly you will get better feedback.  If they don't have to correct your it's vs. its, they can spend time giving you real suggestions.  They will be more likely to respect you and your opinions.

  3. Corollary to #2: Microsoft Word does not know the English language for shit.  Trust its grammar checker at extreme risk.  Computers are lousy at processing natural language.  There is no substitute for your own head.

  4. Starting the actual writing the night before is fine.  It gives you inspiration through terror.  The bigger the paper, the bigger the inspiration.  That's a nice, healthy direct relationship.  It is your friend.

  5. Starting in general the night before is usually not fine.  Writing is the least of the work -- all that pesky research and thinking about your subject is what takes the time.  If you get your information together before you start writing and spend a couple of days mulling it over -- in line at the cafeteria or bank, in the shower, whenever you have a spare second -- the actual writing process won't be nearly as painful.

  6. Forget all that garbage they told you in highschool comp about prewriting -- all that brainstorming, outlining, rough-drafting noise.  Most likely that method doesn't work for you and going through all these steps just results in dragging the paper-writing process out until your brain dies.  Remember, these are the folks who insist that the scientific method has a zillion steps when really there are just two.  The point here is, you want to pare down the process into its least complicated form that still works for you.  If outlines don't help you, the hell with them.  They'll only slow you down.  Hatred of what you're doing is your biggest enemy here, so do your best to avoid it.

  7. Revision often means cutting.  Do not be afraid to let your words go.  If it doesn't belong, kill it.  Do not leave it there simply because you wrote it.  That's padding, and any good teacher will redpen you raw.

  8. The five paragraph essay is not the only form in the world.  The reason they push it so much in beginning comp is that it's a pedagogically useful exercise for beginning writers.  Once you start writing more complex papers (read as: anything you write at university) this form won't be sufficient for what you need to do.

  9. Do not ask, "How long does it have to be?"  This will make your teacher hate you.  If they don't tell you, the answer is, "Long enough."  Figuring out what that means is part of the assignment.

  10. Do not dispute due dates.  This will also make your teacher hate you.

  11. Do not quibble with the assignment, especially not in front of the class.  If you have concerns or want to do something different, grab your teacher after class or during office hours and present your careful, reasoned argument.  Generally assignments are built for a reason, so be prepared to accept it if they reject your proposal.  If you have real problems with an assignment, write something different and accept the consequences.  If you aren't willing to take this gamble, chances are you didn't have a real problem with the assignment.  Often teachers like it when you take little liberties -- it shows you're thinking for yourself and have some confidence in your writing.

  12. When you are done writing you will be unable to do a final proofreading.  Have somebody else do it.  Thank them profusely since what they just did for you was extremely nice.