What I think about an assignment for class varies depending on the assignment and class, but there's a usual process that I have regarding it.
1. How long can I wait before having to do the assignment?
While this sounds irresponsible (and I know full well that it is extremely irresponsible), I find that I work best when I have the most possible time to think about an assignment before doing it, and that I work better under the pressure of an impending deadline. Often I will be going about my business doing something completely unrelated when I figure out exactly how I want to do an assignment (the Wikipedia page that I chose is an example of this, as is the method that I took in doing my Process Critique, and this very journal entry is an excellent example). While my work will occasionally be slightly late, I find that the small penalty for not doing the work on time is much less than the grade I would've gotten had I not done the assignment in this manner.
2. Is the assignment detailed enough?
Often I find that professors will assign papers or projects with little to no explanation of what we are supposed to do. While this usually isn't an issue in the Technical Writing course (for which I am extremely grateful), I have had other courses where the professor will not ever give us a description of what we have to do. One of my CS professors still hasn't given us the project descriptions for the final two projects of the semester with less than a week left, and he barely gave us anything regarding the third project (I completed this after receiving the description for the fourth project, which had information on the third project in it). If the assignment is not detailed enough, then I will try to hound the professor about it until we get something concrete (which varies in its success rate, my CS professor ignores my e-mails and promises in class to give the descriptions out then doesn't do anything about it).
3. Do I know what to do to complete the assignment?
This should be the first thing that comes to mind, but I rarely think about this until I actually sit down to do the assignment. To put it in the words of one of my professors, my talent is inverse to my responsibility. If I actually know what I'm doing I present exemplary work, but whether or not I have learned the material properly in the first place is the real problem that I usually run into.
4. Do I care?
Ties into all three previous steps. Very rarely will I actually care about the assignment given. The reasons for this are numerous, and may include "I already did this in high school/a previous class/I've done this same programming assignment six times now in three different languages!", "I cannot fathom how this can possibly apply to me or seriously aid in my education in any setting, ever", "This is stupid and redundant, surely the professor can find a better use of my time than this.", "No one is going to read this or care", This is too freaking easy!", "I don't get it and I don't really care about getting it", and the ever popular "I'd rather be doing so-and-so or such-and-such". Not caring is my greatest weakness. I know full well that I survive on a scholarship and need to pass the class to maintain it and get a degree, and even with that knowledge I still find caring about anything I deem unimportant extremely difficult.