One way MFA programs provide funding to students is by hiring them as teaching assistants (commonly referred to as TAs) to teach writing classes in exchange for a stipend and, often, tuition remission and health insurance. While each program defines its teaching assistantships differently, in general there are a few things you should know before applying and preparing for one.
A number of creative writing programs give teaching assistantships to all of their incoming graduate students, but others have only a limited number of positions available. Typically program faculty determine which students become TAs based on the overall strength of the creative writing application, plus academic credentials such as undergraduate grade point average and GRE score. Preference is often given to candidates who have previous teaching experience.
The classes TAs teach vary from program to program, but they tend to be undergraduate introductory writing classes of some sort. Typical classes include introduction to literature, composition and rhetoric, and, sometimes, creative writing. TAs usually teach one or two classes a semester on top of their own course load.
Not all new TAs have had experience in the classroom. And those going directly from being an undergrad in the spring to working as a teacher of undergrads in the fall may feel especially intimidated. It's in the best interest of universities to assure that their TAs perform well, so they always provide some kind of training, but the rigor of that training varies. Some programs require TAs to attend pre-semester orientation sessions and sign up for first-semester seminars on how to teach writing. Such classes brief students on what the department expects from its TAs, as well as instructing them on the best practices for creating a syllabus, which texts to use, how to create assignments, how to inspire lively classroom discussion, and grading. Other programs require their students to work as tutors and/or with a faculty member first before taking on their own classes.
Along with taking the required preparatory courses, new TAs should also consider reacquainting themselves with the rules of grammar and punctuation. While most creative writers have an intuitive sense of what constitutes strong prose, they don't always have at the tip of their tongues (or pens) the rules that explain why. Part of teaching introductory writing involves being able to convey these fundamentals to beginning writers, so it helps to give yourself a brushup. Some resources to consider: The Elements of Style by William Strunk (Dover Publications, 2006), The Practical Stylist by Sheridan Baker (Longman, 1997), and Essentials of English Grammar by L. Sue Baugh (McGraw-Hill, 2005).