During the course of your graduate career, the opportunity will likely arise.  You may TA a course, teach a course, or mentor other students.  I've began teaching labs at the University of Texas in 2001, and have been teaching since inside and outside of the classroom.  You can get a better idea of my experience from reading my teaching portfolio, and here are some links and tips I've learned over the years. 

The Last Lecture by Dr. Randy Pausch - I can't begin to tell you how influential this video is to me.  If you're an educator, this video is a must view.  Watch the video, buy the book, incorporate this into your teaching and your life.   This man not only models how to teach, but he also models how to live.  We all need great mentors ( I'm lucky to have an entire handful), and this enthusiastic teacher is one I would like to add to my list, even if it is just through videos.  His life is one to be envied. 

Special thanks to my teaching mentors past and present: Dick Shumer, Dr. Devendra Singh, Dr. Stephen Balfour, and Dr. Ludy T. Benjamin.

Some things I learned over the years:

• Students will never cease to amaze you.  Just when I think I have some pretty bright students in class, another one comes in and surprises me.  Remember the students in Randy Pausch's video?  That's from undergrads!  The more you ask of them, the more they'll give.  The more they give, the more they learn. 
• Undergraduates are humans.  They get exhausted, distracted, and unmotivated.  Don't take it personally if they fall asleep in class or don't come to class.  I remember falling asleep in classes.  I tried so hard to be awake. 
• Undergraduates are not your friends until after grades are turned in.  Before then, they are your students.  Your job is to mentor them, teach them, and to inspire them.  It isn't your job to make them happy.  Disaster ensues the moment they think you are their friend.  Don't let them play that card. 
• Being young, physically small, and female adds specific challenges when teaching large classes.  Students tend to take you less seriously than if you were older, taller, and male.  Stereotypes are a fact of life.  Work with it, not against it.
• Set a standard of classroom behavior the very first day and stick with it.  When you start bending the rules for students, they'll run right over you.
• Prepare for your class as if it was a job interview.  There is no "winging" it when giving a lecture.  And I've been winging talks for AGES.  You can't do that in a class.
• Don't be afraid to admit that you're wrong or that you don't know.  We're humans; we make mistakes.  We may be experts in our niches, but we aren't all knowing.  It's okay to be wrong.
• Make sure you don't have the answers attached to the exams when you have them photocopied.  This happens to someone every semester.  I have nightmares that I've done it sometimes.
• Sometimes undergraduate are just a little shy.  Sometimes when you ask your class a question, they'll look at you dumbfounded.  You wait a while.  No response.  That's okay.  Don't take it as a sign that they aren't paying attention.  I do it sometimes in graduate courses when I didn't think my comments were truly profound or maybe I was commenting too much.  The instructor just thought no one did the readings.