Attend related lectures by the professor. If you are not typically required to attend all of the professor’s lectures, this can help you see how the professor runs the class as well as learn about the students and what they know.
Consider how the professor’s priorities fit into the broader course goals. Especially if you are filling in on short notice, ask if the professor has lecture notes to guide you. As needed, ask about the jargon and exact terms of notation used until that point in the course, to ensure consistency with other lectures.
Locate and read supplemental sources. You may glean interesting and useful examples, supporting research, or organizing themes. Be sure you have clear goals in mind so that you read efficiently for what you need.
Prepare a good outline. A one-page summary can help you see the overall coverage and coherence of your initial plan. Usually, 3-4 major sections is the right amount for a 50-75 minute lecture. You may want to share this outline with the professor to get feedback and to check how much flexibility you have when presenting the material.
Carefully plan visual aids. Well-designed visual aids should clearly reinforce the main ideas and be coordinated with what you say. Be sure that any text is large enough to be seen from the back of the room (usually 18-24 point for transparencies).
Plan ways to interact with students. You will want to get ongoing feedback on their comprehension. Determine how much interaction, discussion, or in-class practice is appropriate for the goals of the lecture. Try to be consistent with the class atmosphere established by the professor. Write out for yourself beforehand at least a few of the questions you plan to ask, to make sure they are clearly worded and answerable.
Review your notes thoroughly. Make sure you feel comfortable and confident in presenting the material. Some lecturers find it useful to include reminders to themselves (e.g., “write student’s responses on this transparency” or “pause for questions”) to make the presentation smooth. Even if you have very good notes from the professor or are familiar with the content, you need to make sure that the level of detail in the notes is what you need.
Mentally rehearse the lecture at least once. In this mental rehearsal, check to make sure that the introduction sets clear goals, that there is a logical transition that connects the major sections, that visual aids highlight your major argument, and that the summary stresses the most important points. Some TAs have found it helpful to practice in front of a mirror.