It takes practice to clearly and engagingly explain technical ideas and to tailor your presentation to your audience. The experience you gain by serving as a teaching assistant is invaluable. For this reason, the department has instituted a requirement that as of Fall 2015, all PhD students are required to serve as a teaching assistant at least one semester during their program of study.
As part of the requirement, the course instructor must give you an opportunity to be in front of a group of students at least once during the course (hopefully more). You will be required to sign up for the course 601.807 (Teaching Practicum) during the semester of your required teaching assistantship. At the end your performance will be evaluated by the course instructor.
The department also strongly encourages PhD students to design and teach their own short courses or to teach their own section of a core course. A short course is a 1-credit course that meets either during intersession (January) or a regular semester for a total of 12 class hours. Teaching a core course section provides the opportunity to collaborate on course content, assignments, and more with other section instructors and at least one regular faculty member while being fully responsible for a regular semester-long course. Both of these types of teaching activity are compensated accordingly.