Back when I was doing my undergrad degree, I almost invariably approached essays the way I was taught to in high school:
1. define your terms
2. take a position
3. write an outline, include relevant quotes
4. write an introduction saying what you are going to say (ie doing all of the above)
5. write the essay, make sure you use quotes, examples
6. write a conclusion, saying what you've said
Point six was always the hardest part for me, since it was hard to make it significantly different to the introduction.
That method worked well enough in high school and still went pretty well for most of my undergrad years. It helps, of course, to have an essay question that you are required to address. As a post grad, I mostly haven't had that benefit.
How I write an essay now:
1. Develop an interest
2. Read as widely as possible
3. Start to narrow down the interest
4. Repeat 2 & 3 ad nauseum
5. Start to write - this may be something by way of an introduction, attempting to set out some parameters for the essay, but it's more likely to be some disparate paragraphs supposedly from the body of the essay; presuming the latter:
6. Try to write an introduction
7. Write some more disparate paragraphs
8. Realise the introduction hasn't captured what I am trying to do at all.
9. Try another introduction
10. 7-9 on repeat, interspersed with much wailing and gnashing of teeth.
11. Finally figure out what I'm trying to say.
12. Write yet another introduction, hopefully capturing 11 above.
13. If 12 works, move on to actually writing essay. Otherwise, go back to 10 above, only moving to the body of the essay when 12 is finally working.
14. Write conclusion - hopefully this flows easily from body of essay, otherwise go back and try again; put gnashing of teeth on repeat.
15. Having written essay, realise that 12 was wrong after all, and re-write introduction again.
16. Tweak body of essay.
17. Repeat several times, then move to 18.
18. Tweak conclusion.
19. After sundry proofing efforts, submit essay.
20. Breathe.
I've been thinking/reading for the essay I am currently working on since last year. It's due for submission in less than a month. Finally, I think I've aced point 12. Or, it could be that I'm still stuck on 10 but just haven't realised it yet. I'm about to try moving on from the introduction (again). Wish me luck.