Go to your student government office on campus or look up that department on your college's website.
Obtain an application to form a new student group or club. Each university will have different terminology and paperwork; you can ask your college's help desk or consult the school's website for specific information.
Find students willing to sign the student union charter. Check the paperwork to make sure you have enough signatures to at least meet the required minimum.
Choose your student union officers and specifically define their roles.
Fill out the rest of the paperwork and turn it back in to your student government office.