Obtain at least a master's degree in video game design. Colleges and universities don't hire teachers unless they meet minimum educational and background requirements.
Have real world experience. If you are the lead game designer on several popular video games you are, more than likely, going to be allowed to teach video game design without a master's degree. For top professionals schools are going to make an exception. Any film school would let Steven Spielberg teach film, even though he didn't receive a bachelors degree until after making a good portion of his movies, and the same is the case for top talent video game designers.
Familiarize yourself with the video game design software the school uses. If you don't know how to use the programming you are going to find it rather difficult to instruct others how to use it. Thankfully, most design programs are similar to one another, so you have a leg up on teaching yourself the new programming.
Explain yourself well. No matter how talented you are, if you can't communicate with others you aren't going to make a very good teacher. Video game design is all about showing individuals how to design their own material, and because most students probably haven't touched the software before you are going to receive a large amount of questions.