How can I introduce myself as an undergraduate teaching assistant to students at my own university?
Usually, the professor of a course will introduce teaching assistants to students on the first day of class. If you are asked to say a few words to introduce yourself, you want to convey professionalism, with a sense of helpfulness but with clear boundaries.
As first impressions count, remember to dress in a "business casual" style -- khakis or nice jeans and a collared shirt rather than a t-shirt and shorts. Give your name, and a bit of your background (your major, where you are in your program) and then describe briefly what you will be doing in the class and how you can help students. You should also describe how students can reach you if they have questions outside class hours.
Set up a teaching e-mail account (you can make a free one on gmail or hotmail if your school won't give you an extra) completely separate from your regular email, but linked to its own GoogleTalk or Skype address. That way you can respond to email queries from students and even hold virtual office hours but in a manner that makes clear boundaries between your role as a teaching assistant and your life as a student.
The main issue you will need to negotiate is how to present yourself as a helpful peer while at the same time remaining separate from the other students in your identity as a teacher.