You must have list eligibility to apply if you are not a current or former state employee! (More Info).
To establish eligibility, review the classification/job title examination bulletin for details on the examination, the type of examination, and the minimum qualifications required to compete in the examination. Examination bulletins are located here. Then, take and successfully pass the examination(s) to get placed on the eligibility list.
Once eligibility has been established, search and apply for a job vacancy. Current job vacancies are located here. Depending on the department, the application submittal and interview requirements may vary.