What are some ways to increase grading speed? I sometimes spend too much time on grading students' homework in the class I am a TA for. I am asking if there are some ways to improve grading speed? I hope that I can learn some useful tips from experienced people here.

For example, which one do you think will be faster, grading student by student, or problem by problem?
I find it very helpful to write a grading rubric.  It includes how many points I give for each part of each problem.  I also include how many points of partial credit I give for various common errors.  Typically, my key consists of a worked copy of the exam, and I make notes about each question on the actual exam.  Generally, my rubric gets more detailed as I grade, since it's only then that I learn what are the common mistakes.

If I feel that I'm taking too long grading, I'll often start timing myself.  Maybe I get at most 30 second per question (often less).  This isn't a hard rule, but it helps me know what to aim for.  (Recently I just graded a calculus exam, so most of the problems were pretty quick to grade.)  Your mileage will vary from one subject to another.