No formal training is necessary if you want to become a script supervisor, but you will need to have certain skills that will make you a more valuable candidate for the position. The script supervisor is responsible for ensuring the continuity of a film, as well as noting changes to the script and ensuring all other elements of the film are consistent throughout. If you want to make yourself a more attractive job candidate, you can take classes that will help you learn the necessary skills to become a script supervisor, but these are not always necessary.
Try to secure a job at a film studio in any capacity. This may mean working as part of the film crew, or it may mean doing clerical work. Having a job at the film studio will often give you inside information about jobs opening up in the future; you may be able to become a script supervisor simply by applying when the position opens up. In most cases, however, you will need to work your way up the ladder by applying for a position as a supervisor's assistant. You will then work with a current script supervisor and assist him or her on the daily duties of the job. This is a great way to learn the techniques and skills necessary to be an effective supervisor.
Once you have worked as an assistant, you will be in better position to become a script supervisor because you will be able to list this experience on your resumé. Still, you will probably need to do some networking and establish contacts within the industry to become a script supervisor. Try to develop a relationship with the film directors, as well as with producers. These are the people that you will work with on a daily basis as a supervisor, so by developing relationships with these people, you are making yourself known as a responsible person who is easy to work with and a good fit for the job.
Be knowledgeable about filmmaking and the process of creating films. The more you know about the process, the more attractive you will be as a job candidate. Learn about the different types of jobs on a film set and know what each person is responsible for. It is a good idea to learn common terminology as well so your learning curve will not be as prolonged once you secure a position; this will help you retain your position and obtain future script supervisor jobs as well.