Some TAs find that swiftly grading a few papers from their set helps them to get a feel for the range of student performance before they settle down to dispatching the rest (returning to the first papers when they have finished). This can be more helpful than agonizing over each of the first few papers you grade.
Some TAs spend an hour scanning as many papers as possible, and then articulate a rubric of important criteria before beginning close evaluative reading and scoring.

As a rule of thumb, you should spend about twenty minutes on each paper.

If you've prepared a statement of grading policy for your students, keep a copy to refer to as you grade; this will help you to be more consistent.

Students appreciate it when you write your comments out in full instead of using lots of abbreviations (spelling? instead of Sp and so on). However, shorthand can save a lot of time and you can give your students a key to your editing symbols to avoid any confusion.

Don't overwhelm the student with an overabundance of comments: two or three areas to focus on per paper is enough.

Some TA's find it's efficient to use a standardized rubric.

You can have students submit a blank cassette tape with their paper. You can then read the paper into a tape recorder, making remarks as you read. This is helpful to students who need to hear how their work is interpreted by their audience. This also limits the amount of time spent on each paper.

Grading into a computer can facilitate the process by making accessible the student's previous grades and comments and streamlining the process. Be sure to save often this is work you will not want to do twice.

Meeting with students individually before the papers are due may help prevent some errors and result in better papers.

The better the paper, the easier it is to grade, but be sure you still give suggestions for improvement even on an A paper. Writing workshops in class serve this purpose as well.

Meeting with students individually and marking their papers with them is another option. Some TAs schedule twenty minute sessions with individual students and mark their papers with the student present. This is a good way to force yourself to keep to a twenty minute limit on each paper. More important, meeting with the student will ensure that the student understands the comments on the paper and has a good idea how to improve his/her work.

One eccentric solution to the grading time-vacuum is the State Street Grading Crawl. Choose a coffee house, grade three papers there, then move to the next coffee house, grade three more, etc. This technique is more popular than you might think. There are fewer distractions in coffee houses than at home and the caffeine eventually builds up in your system to create a sort of grading frenzy. (This technique does NOT work if you bring a friend.)

Feel free to ask your professor or a TA colleague for a second opinion on a paper which poses particular difficulties.

Finally, because grading sometimes can be repetitive, it often helps to take short breaks periodically to ensure consistency of judgment. It's tempting, for example, to be more critical of an interpretation just because you've heard it before. Be consistent in grading similar interpretations.

Beware The End of Quarter Crunch
You should be aware that marking finals and computing final grades will often conflict with your own end-of-the-quarter coursework demands. TAs may find themselves trying to write their own term papers while frantically marking finals at the same time. Obviously, you are ultimately responsible for arranging your schedule so that everything gets done on time, but be aware that the deadline for final grades is not negotiable.