This is a list of typical duties of a TA, as we understand the job. We give for each duty an average number of hours to spend --- but this can vary tremendously from class to class. There is only one thing that we would like to insist on: a TA should never spend too much time on grading. The educative side of the job is much more important.
By far the most time consuming and less rewarding side of the job, grading is probably the original reason why teaching assistants exist --- to alleviate the instructor from this duty. See the page on grading for tips to spend as little time as possible on grading, and why.
Students sometimes ask questions by e-mail. Usually, an email address is setup for the course, and TAs (and sometimes the instructor) alternate in answering the question queue. For particularly large courses with many TAs, answering questions via a class newsgroup can be a good way to coordinate question answering.
The only occasion where the TA can meet face to face with the students, office hours can be very rewarding. Attendance vary greatly depending on whether a homework is due the day after. Students rarely come for enlightments on the class contents, but more often come for hints on the homework.
Be sure to set your office hours at a convenient time for the students. In particular, try to set an office hour the day before the homework is due. Whether we like it or not, it is the time the most in demand. For big classes, it might even be a good idea to have two TAs hold office hours at the same time (in different places).
Another opinion: Setting office hours right before due date is convenient for those who procrastinate. However, it also encourages procrastination. There are a couple good reasons for having office hours a little in advance of due dates:
Not all classes require sections, and sections are typically not mandatory to attend for the students. Sections provide a sample class, where the TA may try his teaching skills, but he should remember that these are intended for interactive problem solving.
Whether or not you are required to go to lecture, it's highly recommended that you go to as many lectures as you can since 1) it allows you to stay up-to-date with what material is presented in class and 2) it makes you visible to the students to show that you care and are interested in the class. You can bring other work to keep you occupied (e.g. answer e-mails, enter grades, etc.,) but check in once and awhile to see what's going on in class.
TAs have more input from the students than the instructor does, and can see from the homeworks how the students are doing. They should not hesitate to give feedback to the instructor.
There is no clear attribution of responsibility on this item. A class web page is a great thing to have, and the teaching assistant should take care of it the instructor doesn't have one yet.
The TAs will maintain the list of grades, and there are various ways to do it. The simpliest is to have a spreadsheet, though the students won't be able to see them and, if you only have one copy, can be easy to lose. If you using Coursework, you'll be able to enter grades there, make them available to the students, and export the grades as a spreadsheet.
The midterm and final, if any, are graded by the TAs and the instructor together. It is customary for the instructor to provide food during the session.