If the prof doesn't tell you, ask about job details: marking schemes, policies, etc. What does the prof care about in student performance? How does the prof expect you to screen for plagiarism? Strive for consistency between yourself and the prof from the student's point of view.
Strive for consistency in your marking. Students value fairness.
Make sure the student knows how the mark could have been improved.
Do your marking and teaching from the students' point of view. Don't just show them how to get a valid answer: start with their work and show them where they went off the track so that they can improve their mental model of the topic at hand.
Within your prof's guidelines, do not hesitate to give out low grades. (Some TAs are very reluctant to give out low grades. None of us likes to do this, but you do students a disservice by rewarding poor work!)
Report patterns of student problems (errors, misunderstandings, etc.) to the prof. Some changes in lectures or teaching materials may be necessary.
Communication is important. Train students to communicate well. Help students learn the precise use of technical vocabulary. Model this yourself. Work on communication especially hard if English is not your native language.
Try to improve your teaching skills. Put yourself in the student's shoes: What does this person understand now, where are the gaps, and how can I move the student from where s/he is to where I want him/her to be? What does this student's question tell me about his/her understanding of the topic?
TA work will be a learning experience for you. It may shape your own career. Give it the importance it deserves.
If you're not sure, talk to the prof. It's OK to admit that you don't know the answer. Many of us are human. We were TAs once, too!
Most importantly, get in touch with the University's Centre for Learning and Teaching (CLT):