Organizing Your Class
Your lecturer should have a syllabus, and ideally you should have a copy of it before the course begins. It is not unusual to get a copy at the same time as the students. You should also have a syllabus for your discussion section. Do not write or present your syllabus before the lecturer. Wait until you know exactly how they want to do things, since their policies trump yours.
A syllabus is more than a list of dates and topics. It should include your contact information (name, office number, office phone, e-mail), your office hours, policies, grading scheme for your discussion section, etc. The lecturer decides policies first. Your policies cannot contradict the lecturer's policies. If you have a problem with your lecturer's policies, discuss it with them outside of class or talk about it with your TA coordinator. You talk about your syllabus in class and give your students a hard copy. This is everything you can realistically do to make this information available to the students. It also prevents them from saying, "But I didn't know..."
A course web page, for one, is a great place to keep a copy of your syllabus. In general, it can be an invaluable resource. It is a readily available place for students to find out about policies, assignments, test dates, etc. If you have no idea how to make a web site, start here or ask someone who does. Even though you aren't required to make a course page, it is very easy, it is good professional development, and you will be doing your students a huge favor.
You must have 3 or more set office hours per week. Decide what these hours are at the beginning of the semester and stick to them. It is okay to choose these hours to fit your schedule, but try not to be unreasonable. It is impossible to find a set of hours that every one of your students can use, so "by appointment" is also a fair option for one of your hours. There may be times in which none of your students show, so it's OK to use that time to do your own things, as long as you can easily be found and your students are your first priority for that hour.
Office hours are a chance for students to get extra help, to make up quizzes (if you allow this) or to discuss sensitive matters. You do not have to have perpetual office hours. It's okay to tell a student they have to leave once your office hours end. Similarly, e-mail is a great way for students to contact you, but you do not have to answer their mail on a 24-7 basis. If you decide to use e-mail as a way of hearing from your students, announce a response policy - e.g. 'E-mails received by 9:00PM weekdays will get a response by 9:00PM the next day.
A classlist is an email list for your section that is automatically created for you by DoIT. It is a great way to communicate with your students about assignments, changes in the syllabus, and other announcements. It is also a great way for students to discuss questions or organize study groups.
Although the list is automatically created for you, it won't work until you enable it. All enrolled students are automatically members of the list, and anyone who drops will disappear from the list within a day of dropping. An email will automatically be sent to you when your classlist has been created with instructions on how to enable it. You can also enable your classlist and make changes (add guests, opt not to receive mail, etc.) by logging into MyUW , then clicking on the "Academics" tab, and selecting the "Faculty Center." Once there, select the appropriate semester, and then click on the roster of the section you want. There will be two tabs for the roster: a Class Roster tab and an Email tab. Click on the email tab and you will get the roster with all your students' email addresses. At the top is a link called "Enable and Modify Your Classlist." From there it's pretty easy to navigate.
Note that you are not the only administrator of the list; the lecturer for the course is also listed as an administrator and a list member. Unless your lecturer opts out of receiving email from your classlist, he or she will get every email you or your students send to it. (The lecturer also has a classlist for the whole lecture, so you might want to mention to him or her the option to not receive mail from all the smaller classlists.)
Incomplete/Late work, Missed Quizzes ...
These are the sorts of topics that should be addressed in your syllabus. They are also the sorts of topics where your lecturer decides first. If your lecturer does not have a policy regarding late work, etc. then you may set your own policy.
Different TA's set different policies. You can deduct points for lateness, simply refuse late work or extend amnesty up to a certain deadline (test dates, for example). Similarly, with quizzes, some TA's do not let students take missed quizzes, but will drop the lowest two quiz grades. Others will allow students to take a missed quiz if the student informs them in advance of an absence. Whatever policy you choose, decide on it in advance (since actual requests always come at maximally inconvenient times) and stick to it unless confronted with a truly extraordinary case.
One last consideration with homework is that grading it consistently and returning it promptly should be high on your list of priorities. Both of these goals are much easier to achieve if you grade each assignment as a batch and much harder if you have to keep track of many students' late work.